bluuebunny/crossref_metadata_2025 huggingface dataset:
Completely Reducible Operator Algebras and Spectral Synthesis
Authors: Rosenoer Shlomo
Published: December 2010

An algebra of bounded operators on a Hilbert space H is said to be reductive if it is unital, weakly closed and has the property that if M ⊂ H is a (closed) subspace invariant for every operator in , then so is M⊥. Loginov and Šul'man [6] and Rosenthal [9] proved that if is an abelian reductive algebra which commutes with a compact operator K having a dense range, then is a von Neumann algebra. Note that in this case every invariant subspace of is spanned by one-dimensional invariant subspaces. Indeed, the operator KK* commutes with . Hence its eigenspaces are invariant for , so that H is an orthogonal sum of the finite-dimensional invariant subspaces of From this our claim easily follows.
Non Commutative Lp Spaces II
Authors: Katavolos A.
Published: December 2010

Let M be a w*-algebra (Von Neumann algebra), τ a semifinite, faithful, normal trace on M. There exists a w*-dense (i.e., dense in the σ(M, M*)-topology, where M* is the predual of M) *-ideal J of M such that τ is a linear functional on J, and

(where |x| = (x*x)1/2) is a norm on J. The completion of J in this norm is Lp(M, τ) (see [2], [8], [7], and [4]).

If M is abelian, in which case there exists a measure space (X, μ) such that M = L∞(X, μ), then Lp(X, τ) is isometric, in a natural way, to Lp(X, μ). A natural question to ask is whether this situation persists if M is non-abelian. In a previous paper [5] it was shown that it is not possible to have a linear mapping
The Radii of Polyhedrons
Authors: Enns T. C.
Published: December 2010

1. Introduction. Let P be a polyhedron (i.e., a 3-dimensional polytope). A path in P is defined as a sequence of edges (x1, x2), …, (xi−1, xi), (xi, xi−1), …, (xn−1, xn) where (xi, xi+1) denotes the edge with endpoints Xi and Xi+1. Define the length |A| of a path A to be the number of edges of said path. The distance between any two vertices x and y of P is defined to be the least length of all paths of P between x and y. For the purposes of this paper, if x and y lie on a particular path A, the distance between x and y along A will be defined to be the length of the segment of A between x and y. The radius of P is defined to be the smallest integer r for which there exists a vertex v of P such that the distance from v to any other vertex of P is at most r.
Amenability and Translation Experiments
Authors: Paterson Alan L. T.
Published: December 2010

In [11] it is shown that the deficiency of a translation experiment with respect to another on a σ-finite, amenable, locally compact group can be calculated in terms of probability measures on the group. This interesting result, brought to the writer's notice by [1], does not seem to be as wellknown in the theory of amenable groups as it should be. The present note presents a simple proof of the result, removing the σ-finiteness condition and repairing a gap in Torgersen's argument. The main novelty is the use of Wendel's multiplier theorem to replace Torgersen's approach which is based on disintegration of a bounded linear operator from L1(G) into C(G)* for G σ-finite (cf. [5], VI.8.6). The writer claims no particular competence in mathematical statistics, but hopes that the discussion of the above result from the “harmonic analysis” perspective may prove illuminating.

We then investigate a similar issue for discrete semigroups. A set of transition operators, which reduce to multipliers in the group case, is introduced, and a semigroup version of Torgersen's theorem is established.
Weighted and Subsequential Ergodic Theorems
Authors: Baxter J. R. , Olsen J. H.
Published: December 2010

1. Introduction. Let (X, , μ) be a probability space, T a linear operator on ℒp(X, , μ), for some p, 1 ≦ p ≦ ∞. Let an be a sequence of complex numbers, n = 0, 1, …, which we shall often refer to as weights. We shall say that the weighted pointwise ergodic theorem holds for T on ℒp, if, for every ƒ in ℒp,

1.1

Let a denote the sequence (an). If (1.1) holds we shall say that a is Birkhoff for T on ℒp, or, more briefly, that (a, T) is Birkhoff.

We are also interested in ergodic theorems for subsequences. Let n(k) be a subsequence. We shall say the pointwise ergodic theorem holds for the subsequence n(k) and the operator T if, for every ƒ in ℒp,

1.2
Hopf Algebras from Branching Rules
Authors: Hoffman P.
Published: December 2010

Below we work out the algebra structure of some Hopf algebras which arise concretely in restricting representations of the symmetric group to certain subgroups. The basic idea generalizes that used by Adams [1] for H*(BSU). The question arose in discussions with H. K. Farahat. I would like to thank him for his interest in the work and to acknowledge the usefulness of several stimulating conversations with him.

1. Review and statement of results. A homogeneous element of a graded abelian group will have its gradation referred to as its dimension. In all such groups below there will be no non-zero elements with negative or odd dimension. A graded algebra (resp. coalgebra) will be associative (resp. coassociative), strictly commutative (resp. co-commutative) and in dimension zero will be isomorphic to the ground ring F, providing the unit (resp. counit). We shall deal amost entirely with F = Z or F = Z/p for a prime p; the cases F = 0 or a localization of Z will occur briefly. In every case, the component in each dimension will be a finitely generated free F-module, so dualization works simply.
Unitarily Invariant Operator Norms
Authors: Fong C.-K. , Holbrook J. A. R.
Published: December 2010

1.1. Over the past 15 years there has grown up quite an extensive theory of operator norms related to the numerical radius

1

of a Hilbert space operator T. Among the many interesting developments, we may mention:

(a) C. Berger's proof of the “power inequality”

2

(b) R. Bouldin's result that

3

for any isometry V commuting with T;

(c) the unification by B. Sz.-Nagy and C. Foias, in their theory of ρ-dilations, of the Berger dilation for T with w(T) ≤ 1 and the earlier theory of strong unitary dilations (Nagy-dilations) for norm contractions;

(d) the result by T. Ando and K. Nishio that the operator radii wρ(T) corresponding to the ρ-dilations of (c) are log-convex functions of ρ.
Asymptotic Behaviour of Nonoscillatory Equations
Authors: Edelson Allan L. , Perri Emilia
Published: December 2010

For nonlinear equations of the form

I

there has been considerable interest in determining the asymptotic forms of nonoscillatory solutions. We assume r(t) is continuous and positive on [0, ∞), and f(t, x) is continuous on [0, ∞) × R, and f(t, x) ≥ 0 for x ≠ 0. For n = 2, equation (I) was studied by Kusano and Naito [3], who found necessary and sufficient conditions for the existence of minimal and maximal nonoscillatory solutions. The former are the bounded solutions, while the later are those asymptotic to the function

1.1

Their method consisted of writing (I) in the form of an integral operator and applying the Schauder fixed point theorem. For arbitrary n, but for r(t) = 1, Kreith [2] found necessary and sufficient conditions for the existence of maximal solutions.
Local Stability and Saturation in Spaces of Orderings
Authors: Schwartz Niels
Published: December 2010

If k is a f.r. (= formally real) field which is partially ordered with positive cone, P, XP denotes the space of total orders T of k with P ⊂ T. Suppose you have a subset A ⊂ XP and an element T ∈ XP, T ∉ A. Then the main question investigated in this paper is the following: How can T be separated from A by using elements of k? To be more specific, this is split up into two different questions.

Question 1. Suppose A is closed. Then there is an n ∈ N and elements a1, …, an ∈ k such that the basic open set H = H(a1, …, an) is a neighborhood of T and has empty intersection with A. Now, if T is given, what is the least n ∊ N (if it exists) such that T has a neighborhood basis consisting of basic open sets of the form H(a1, …, an)?
Ergodic Properties of Lamperti Operators, II
Authors: Kan Charn-Huen
Published: December 2010

For T in our main Theorem 5, T* is called Lamperti in [11], whose terminology and notation we shall follow in the sequel. To avoid longish expressions, we shall also say that T* here is disjunctive and, dually, T = (T*)* is codisjunctive. The present work grows out of an attempt to establish a DEE for the general power bounded positive operator on Lp, in view of the success in the contraction case [1, 11], and forms a continuation of [11]. (In passing, we note that Calderon's technique [2] mentioned in [11] was anticipated in 1938 by M. Fukamiya [7], though in a variant form and for a more classical case, namely that of a positive Lp isometry induced by an invertible, measure preserving transformation on a totally finite measure space. Calderon's case does not assume invertibility nor total finiteness.)
Secant Spaces to Curves
Authors: von Zur Gathen Joachim
Published: December 2010

A classical question in algebraic geometry is whether a given projection of a projective space induces an isomorphism on a given closed subvariety. To answer it, one investigates secant lines to the subvariety. There has been a lot of recent activity in this field ([12], [14],[18], [21], [23]): see [14] and [12] for references).

An obvious generalization of the secant lines is provided by the secant r-planes, which intersect a given closed subvariety in r + 1 linearly independent points. The closure of the set of these secant r-planes is the secant variety, and the aim of this paper is to determine its rational equivalence class in the case of curves. There is an extensive classical literature about this problem.
On the Uniqueness of the Coefficient Ring in a Group Ring
Authors: Adjaero Isabelle , Spiegel Eugene
Published: December 2010

LetR1andR2be commutative rings with identities,Ga group andR1GandR2Gthe group ring ofGoverR1andR2respectively. The problem that motivates this work is to determine what relations exist betweenR1andR2ifR1GandR2Gare isomorphic. For example, is the coefficient ringR1an invariant ofR1G? This is not true in general as the following example shows. LetHbe a group and

IfR1is a commutative ring with identity andR2=R1H,then

butR1needn't be isomorphic toR2.

Several authors have investigated the problem whenG= , the infinite cyclic group, partly because of its closeness toR[x],the ring of polynomials overR.
Some Congruences for Generalized Euler Numbers
Authors: Gessel Ira M.
Published: December 2010

The generalized Euler numbers may be defined by

Since is zero unless m divides n, we shall write for . Leeming and MacLeod [12] recently gave some congruences for these numbers. They found congruences (mod 16) for where m = 3, 6, 8, 12, and 16. Thus for m = 3, their congruence is

They also proved that , and , and they made several conjectures which may be stated as follows:

C1

C2

C3

C4
Behrend's Theorem for Dense Subsets of Finite Vector Spaces
Authors: Brown T. C. , Buhler J. P.
Published: December 2010

The “combinatorial line conjecture” states that for all q ≧ 2 and there exists such that if , X is a q-element set, and A is any subset of X n (= cartesian product of n copies of X) with more than elements (that is, A has density greater than ), then A contains a combinatorial line. (For a definition of combinatorial line, together with statements and proofs of many results related to the combinatorial line conjecture, including all those results mentioned below, see [5]. Since we are not directly concerned with combinatorial lines in this paper, we do not reproduce the definition here.)

This conjecture (which is a strengthened version of a conjecture of Moser [7]), if true, would bear the same relation to the Hales-Jewett theorem that Szemerédi's theorem bears to van der Waerden's theorem.
Injectives and Projectives in Term Finite Varieties of Algebras
Authors: McNulty George F. , Nordahl T. , Scheiblich H. E.
Published: December 2010

Let V be a class of similar algebras. An algebra is V-injective provided and whenever and fis a one-to-one homomorphism from into and g is a homomorphism from into , then there is a homomorphism h from into such that h º f = g. So is injective provided all diagrams of the following sort can be completed.

Dually, is V-projective provided and whenever and f is a homomorphism from onto and g is a homomorphism from into , then there is a homomorphism h from into such that f º h = g. So is projective provided all diagrams of the following sort can be completed:

This usage of the words “projective” and “injective” differs somewhat from the usage current in category theory.
Global Positive Solutions of Semilinear Elliptic Equations
Authors: Noussair Ezzat S. , Swanson Charles A.
Published: December 2010

The semilinear elliptic boundary value problem

1.1

will be considered in an exterior domain Ω ⊂ Rn, n ≥ 2, with boundary ∂Ω ∊ C2 + α, 0 < α < 1, where

1.2

Di = ∂/∂xi, i = 1, …, n. The coefficients aij, bi in (1.2) are assumed to be real-valued functions defined in Ω ∪ ∂Ω such that each , , and (aij(x)) is uniformly positive definite in every bounded domain in Ω. The Hölder exponent α is understood to be fixed throughout, 0 < α < 1 . The regularity hypotheses on f and g are stated as H 1 near the beginning of Section 2.
λ-Mappings Between Representation Rings of Lie Algebras
Authors: Moody R. V. , Pianzola A.
Published: December 2010

In [10] Patera and Sharp conceived a new relation, subjoining, between semisimple Lie algebras. Our objective in this paper is twofold. Firstly, to lay down a mathematical formalization of this concept for arbitrary Lie algebras. Secondly, to give a complete classification of all maximal subjoinings between Lie algebras of the same rank, of which many examples were already known to the above authors.

The notion of subjoining is a generalization of the subalgebra relation between Lie algebras. To give an intuitive idea of what is involved we take a simple example. Suppose is a complex simple Lie algebra of type B2. Let be a Cartan subalgebra of and Δ the corresponding root system. We have the standard root diagram

Inside B2 there lies the subalgebra A1 × A1 which can be identified with the sum of and the root spaces corresponding to the long roots of B2.
Dense Subspaces of Product Spaces
Authors: Terada Toshiji
Published: December 2010

Unless otherwise specified, all spaces considered here are regular T1-spaces. A space X is called σ-discrete if X is the union of a countable family of discrete subspaces. Arhangel'skii [2] showed that the class of spaces which contain dense σ-discrete subspaces is productive. The fact that the class of spaces which contain dense subspaces of countable pseudocharacter is productive is obtained by Amirdzanov [1]. On the other hand, the class of spaces which contain metrizable spaces as dense subspaces is obviously not productive. As a generalized concept of metrizable spaces there is the concept of σ-spaces [14]. This class of spaces has many similar properties to the class of metrizable spaces. However we will point out a remarkable difference between the class of metrizable spaces and the class of σ-spaces by showing that the class of spaces which contain σ-spaces as dense subspaces is productive.
Spaces with a Unique Uniformity
Authors: Warren Richard H.
Published: December 2010

The major results in this paper are nine characterizations of completely regular spaces with a unique compatible uniformity. All prior results of this type assumed that the space is Tychonoff (i.e., completely regular and Hausdorff) until the appearance of a companion paper [9] which began this study. The more important characterizations use quasi-uniqueness of R1-compactifications which relate to uniqueness of T2-comPactifications. The features of the other characterizations are: (i) compact subsets linked to Cauchy filters, (ii) C- and C*-embeddings, and (iii) lifting continuous maps to uniformly continuous maps.

Section 2 contains information on T0-identification spaces which we will use later in the paper. In Section 3 several properties of uniform identification spaces are developed so that they can be used later. The nine characterizations are established in Section 4. Also it is shown that a space with a unique compatible uniformity is normal if and only if each of its closed subspaces has a unique compatible uniformity.
Maximal d-Ideals in a Riesz Space
Authors: Huijsmans Charles B. , de Pagter Ben
Published: December 2010

We recall that the ideal I in an Archimedean Riesz space L is called a d-ideal whenever it follows from ƒ ∊ I that {ƒ}dd ⊂ I. Several authors (see [4], [5], [6], [12], [13], [15] and [18]) have considered the class of all d-ideals in L, but the set ℐd of all maximal d-ideals in L has not been studied in detail in the literature. In [12] and [13] the present authors paid some attention to certain aspects of the theory of maximal d-ideals, however neglecting the fact thatℐd, equipped with its hull-kernel topology, is a structure space of the underlying Riesz space L.

The main purpose of the present paper is to investigate the topological properties of ℐd and to compare ℐd to other structure spaces of L, such as the space of minimal prime ideals and the space of all e-maximal ideals in L (where e > 0 is a weak order unit).
Three Theorems on the Growth of Entire Transcendental Solutions of Algebraic Differential Equations
Authors: Strelitz Sh.
Published: December 2010

G. Polya [4] has posed the problem as to whether there are entire transcendental functions of order zero satisfying an algebraic differential equation with rational coefficients. G. Polya himself showed that this is impossible for a first order algebraic differential equation. The general problem is now completely solved. G. Valiron demonstrated an example of a third order algebraic differential equation with an entire transcendental solution of order zero (Theorem 1); V. V. Zimogljad (Theorem 2) proved that every entire transcendental solution of a second order algebraic differential equation is of a positive order. It seems to us expedient to bring these results all together. We give here a proof of Theorem 2 different from and in our view simpler than that of V. V. Zimogljad. Theorem 3 refines the results of G. Polya (and of others, see for example [10]) and establishes an exact lower bound for the order of an arbitrary entire transcendental solution satisfying a first order algebraic differential equation.
Pro-Categories and Multiadjoint Functors
Authors: Tholen Walter
Published: December 2010

For a functor G:𝒜→𝔛 and a class 𝔇 of small categories containing the terminal category 1 we form the extension

and call G right 𝔇-pro-adjoint if and only if Pro (𝔇, G) is right adjoint. Here Pro (𝔇, 𝒜) is the completion of 𝒜with respect to 𝔇; it coincides with the usual pro-category of 𝒜 in case 𝔇 = directed sets. For this 𝔇 a full embedding Gis dense in the sense of Mardešić [11] if and only if it is right 𝔇-pro-adjoint in the above sense; this has been proved recently by Stramaccia [15]. The most important example is the embedding of the homotopy category of pointed CW-complexes into the homotopy category of pointed topological spaces (cf. [2]).
Products of Reflections in the Group SO*(2n)
Authors: Djoković Dragomir Ž. , Malzan Jerry
Published: December 2010

Let SO*(2n) be the group of quaternionic n × n matrices A satisfying A*JA = J, where J is a fixed skew-hermitian invertible matrix. An element R ∊ SO*(2n) is called a reflection if R2 = In and R — In has rank one. We assume that n ≧ 2, in which case S*(2n) is generated by reflections. The length of A ∊ SO*(2n) is the smallest integer k(≧0) such that A can be written as A = R1R2 … Rk where R1, …, Rk are reflections. In this paper, for each A ∊ SO*(2n), we compute its length l(A). Set r(A) = rank (A — In). Already in Section 3 we are able to show that the difference δ = l(A) – r(A) can take only three values 0, 1, or 2. The remainder of the paper deals with the problem of separating these three possibilities. The main results are stated in Section 4 and proved in Section 6. The intermediate Section 5 consists of a sequence of lemmas which are needed for the proof. Clearly l(A) depends only on the conjugacy class of A and the main results in Section 4 are stated in terms of conjugacy classes. For the description of conjugacy classes in SO*(2n) we refer the reader to [1]. The present paper relies heavily on our previous paper [5] where the analogous problem was solved for the groups U(p, q). It is worth remarking that only the various lemmas from that paper were used but not the main theorem.
A Class of Homomorphisms of Pre-Hjelmslev Groups
Authors: Knüppel Frieder
Published: December 2010

E. Salow [8] introduced the concept of pre-Hjelmslev groups, a generalization of F. Bachmann's Hjelmslev groups [1] which leads to a more natural theory of homomorphisms and permits a simpler construction of algebraic models. Basically, both types of groups are the groups of motions of a metric plane, the so-called group plane. In such a plane there is a unique perpendicular through any point to any line and the product of three collinear points (three copunctal lines) is a point (a line). Our first section contains the precise definitions and some basic facts.

The homomorphic image of a pre-Hjelmslev group can be more complicated than the pre-image. For instance, there may always be a unique line through two distinct points of the pre-image but not of the image. We study regular homomorphisms of pre-Hjelmslev groups, i.e., homomorphisms with the following property: If two lines intersect at exactly one point, their images will also have precisely one point in common.
Fixed Points as Equations and Solutions
Authors: Adámek Jiří , Merzenich Wolfgang
Published: December 2010

In the literature about the definition of data types there exist many approaches using some concept of fixed point. Wand [13] and Lehmann, Smyth [9] e.g. constructed data types as least fixed points of functors F:K → K. Arbib and Manes [3] showed that some data types turn out to be the greatest fixed points of such endofunctors. In this paper we regard least and greatest fixed points that have a given property.
Range Sets And Bmo Norms of Analytic Functions
Authors: Kobayashi Shoji
Published: December 2010

In this paper we are concerned with the space BMOA of analytic functions of bounded mean oscillation for Riemann surfaces, and it is shown that for any analytic function on a Riemann surface the area of its range set bounds the square of its BMO norm, from which it is seen as an immediate corollary that the space BMOA includes the space AD of analytic functions with finite Dirichlet integrals.

Let R be an open Riemann surface which possesses a Green's function, i.e., R ∉ OG, and f b e an analytic function defined on R. The Dirichletintegral DR(f) = D(f) of f on R is defined by

1.1

and we denote by AD(R) the space of all functions f analytic on R for which D(f) < +∞.
On Isomorphisms of Lattices of Closed Subspaces
Authors: Fillmore P. A. , Longstaff W. E.
Published: December 2010

By a projectivityof vector spaces Xand Yover fields F and G is meant an isomorphism Ψ:(X) → (Y) of their lattices of subspaces. A basic theorem of projective geomtry [2, p. 44] asserts that, for spaces of dimension at least 3, any such projectivity is of the form Ψ(M) = SM for a bijection S:X → Y which is semi-linear in the sense that S is an additive mapping for which there exists an isomorphism σ:F→ G such that

S(λx) = σ(λ)Sx for all λ ∈ Fand all x∈ X.

In [12] Mackey obtained a continuous version of this result: for real normed linear spaces Xand Y, the lattices and of closed subspaces are isomorphic if and only if X and Yare isomorphic (i.e., via a bicontinuous linear bijection).
Equicontinuity of Families of Convex and Concave-Convex Operators
Authors: Jouak Mohamed , Thibault Lionel
Published: December 2010

J. M. Borwein has given in [1] a practical necessary and sufficient condition for a convex operator to be continuous at some point. Indeed J. M. Borwein has proved in his paper that a convex operator with values in an order topological vector space F (with normal positive cone F+) is continuous at some point if and only if it is bounded from above by a mapping which is continuous at this point. This result extends a previous one by M. Valadier in [16] asserting that a convex operator is continuous at a point whenever it is bounded from above by an element in F on a neighbourhood of the concerned point. Note that Valadier's result is necessary if and only if the topological interior of F+ is nonempty. Obviously both results above are generalizations of the classical one about real-valued convex functions formulated in this context exactly as Valadier's result (see for example [5]).
Some Spectral Properties of Polar Decompositions
Authors: Cain Bryan E.
Published: December 2010

The results in this paper respond to two rather natural questions about a polar decomposition A = UP, where U is a unitary matrix and P is positive semidefinite. Let λ1, …, λn be the eigenvalues of A. The questions are:

(A) When will |λ1|, …, |λn| be the eigenvalues of P?

(B) When will λ1/|λ1|, …, λn/|λn| be the eigenvalues of U?

The complete answer to (A) is “if and only if U and P commute.” In an important special case the answer to (B) is “if and only if U2 and P commute.“

Since these matters are best couched in terms of two different inertias, we begin with a unifying definition of inertia which views all inertias from a single perspective.

For each square complex matrix A and each complex number z let m(A, z) denote the multiplicity of z as a root of the characteristic polynomial
Discrete Open and Closed Mappings on Generalized Continua and Newman's Property
Authors: McAuley Louis F. , Robinson Eric E.
Published: December 2010

In 1930, M. H. A. Newman proved a rather remarkable theorem which has become one of the classical theorems in topology. It has many important applications. A special case of Newman's Theorem is that a periodic homeomorphism of periodn> 1 of a sphereSonto itself must have some orbit which is not contained in a “cap” smaller than a hemisphere. The general theorem is as follows:

THEOREM ([15]).Suppose that Mnis a connected (metric) n-manifold, U is a domain in Mn, andp is an integer greater than1.Then there is a positive number d such that no uniformly continuous homeomorphism h of Mnonto itself of period p moves every point of U a distance < d. That is, there is x ∊ U so that the orbit of x under h has diameter ≦ d.
Subclasses of Starlike Functions Subordinate to Convex Functions
Authors: Silverman H. , Silvia E. M.
Published: December 2010

Let S denote the class of functions of the form

that are analytic and univalent in the unit disk Δ = {z:|z| < 1}, with S*(α) and K(α) designating the subclasses of S that are, respectively, starlike of order a and convex of order α, 0 ≦ α < 1. If f(z) and g(z) are analytic in Δ, we say that f(z) is subordinate to g(z), written f ≺ g, if there exists a Schwarz function w(z), w(0) = 0 and |w(z)| < 1 in Δ, such that f(z) = g(w(z)). A function f(z) = z + … is said to be in S*[A, B] if

(1)

and in K[A, B] if

(2)
Resultats Nouveaux sur les Faisceaux Quasi-Unipotents
Authors: Mathieu Philippe
Published: December 2010

Dans cette note, nous donnons une réponse à un problème posé dans [5]: nous démontrerons que le niveau de quasi-unipotence de la monodromie avec coefficients est le meilleur possible (voir le paragraphe 2 pour l'énoncé précis).

1. Faisceaux quasi-unipotents. Nous rappelons ici la définition et les propriétés fondamentales de ces faisceaux (voir [3], cf. [5]).

Par D nous désignons un disque ouvert de C centré à l'origine et de
rayon aussi petit qu'on veut. Un faisceau V lisse (ou, suivant une autre terminologie, localement constant) constructible sur D* = D – {0} est dit quasi-unipotent (de niveau d) si la monodromie T opérant sur la fibre générique de V vérifie (Ta – 1)b = 0, où a et b sont des entiers non-négatifs (et b ≦ d).

Définition (1.1). Soient X un espace analytique, Y un sous-espace analytique de X, et V un faisceau constructible sur X – Y.
Geometric and Topological Properties of Certain w* Compact Convex sets which Arise from the Study of Invariant Means
Authors: Granirer Edmond E.
Published: December 2010

Let E be a Banach space, A a subset of its dual E*.x0 ∊ A is said to be a w*Gδ point of A if there are xn ∊ E and scalars γn, n = 1,2, 3 … such that

Denote by w*Gδ{A} the set of all w*Gδ points of A.
If S is a semigroup of maps on E* and K ⊂ E*, denote by

i.e., the set of points x* in the w*closure of K which are fixed points of S (i.e., sx* = x* for each s in S}. An operator will mean a bounded linear map on a Banach space and Co B will denote the convex hull of B ⊂ E.
On Convergence of Vector valued Pramarts and Subpramarts
Authors: Frangos Nikos E.
Published: December 2010

In [15] Millet and Sucheston introduced the notion of pramart and subpramart indexed by directed sets, generalizing that of martingale and submartingale, and studied their properties. In particular convergence theorems were proved. In this note we obtain convergence theorems for analogous Banach-valued processes.

Let E be a Banach lattice with the Radon-Nikodym property. Let (Xt, , t ∊ J) be an E+-valued subpramart of class (d). Precise definitions are given below (Section 1).

In [10] for J = N, Egghe proved a subpramart convergence theorem under the additional assumption that there is a subsequence {nk} ⊆ N such that converges weakly for each .
Optimization and α-Disfocality for Ordinary Differential Equations
Authors: Essén M.
Published: December 2010

For f ∊ L−1(0, T), we define the distribution function

where T is a fixed positive number and |·| denotes Lebesgue measure. Let Φ:[0, T] → [0, m] be a nonincreasing, right continuous function. In an earlier paper [3], we discussed the equation

(0.1)

when the coefficient q was allowed to vary in the class

We were in particular interested in finding the supremum and infimum of y(T) when q was in or in the convex hull Ω(Φ) of (see below).
Differentiation of Multiparameter Superadditive Processes
Authors: Çömez Doğan
Published: December 2010

In this article our purpose is to prove a differentiation theorem for multiparameter processes which are strongly superadditive with respect to a strongly continuous semigroup of positive L1 contractions (see Section 1 for definitions).

Recently, the differentiation theorem for superadditive processes with respect to a one-parameter semigroup of positive L1-contractions has been proved by D. Feyel [9]. Another proof is given by M. A. Akçoğlu [1]. R. Emilion and B. Hachem [7] also proved the same theorem, but with an extra assumption on the process (see also [1]). The proof of this theorem for superadditive processes with respect to a Markovian semigroup of operators on L1 is given by M. A. Akçoğlu and U. Krengel [4]. Thus [1] and [9] extend the result of [4] to the sub-Markovian setting. Here we will obtain the multiparameter sub-Markovian version of this theorem, namely Theorem 3.17 below
Naturally Reductive Homogeneous Riemannian Manifolds
Authors: Gordon Carolyn S.
Published: December 2010

The simple algebraic and geometric properties of naturally reductive metrics make them useful as examples in the study of homogeneous Riemannian manifolds. (See for example [2], [3], [15]). The existence and abundance of naturally reductive left-invariant metrics on a Lie group G or homogeneous space G/L reflect the structure of G itself. Such metrics abound on compact groups, exist but are more restricted on noncompact semisimple groups, and are relatively rare on solvable groups. The goals of this paper are

(i) to study all naturally reductive homogeneous spaces of G when G is either semisimple of noncompact type or nilpotent and

(ii) to give necessary conditions on a Riemannian homogeneous space of an arbitrary Lie group G in order that the metric be naturally reductive with respect to some transitive subgroup of G.
A q-Extension of Feldheim's Bilinear Sum for Jacobi Polynomials and Some Applications
Authors: Rahman Mizan
Published: December 2010

The main objective of this paper is to find useful q-extensions of Feldheim's [6] bilinear formula for Jacobi polynomials, namely,

1.1

where the Appel function F4 is defined by

1.2

α1, α2, ρ are arbitrary complex parameters such that the series on both sides of (1.1) are convergent, and

1.3

is the Jacobi polynomial of degree k, (a)k being the usual shifted factorial.
Groups with Finite Dimensional Irreducible Multiplier Representations
Authors: Holzherr A. K.
Published: December 2010

Let G be a locally compact group and ω a normalized multiplier on G. Denote by V(G) (respectively by V(G, ω)) the von Neumann algebra generated by the regular representation (respectively co-regular representation) of G. Kaniuth [6] and Taylor [14] have characterized those G for which the maximal type I finite central projection in V(G) is non-zero (respectively the identity operator in V(G)).

In this paper we determine necessary and sufficient conditions on G and ω such that the maximal type / finite central projection in V(G, ω) is non-zero (respectively the identity operator in V(G, ω)) and construct this projection explicitly as a convolution operator on L2(G). As a consequence we prove the following statements are equivalent,

(i) V(G, ω) is type I finite,

(ii) all irreducible multiplier representations of G are finite dimensional,

(iii) Gω (the central extension of G) is a Moore group, that is all its irreducible (ordinary) representations are finite dimensional.
On the Definition of C*-Algebras II
Authors: Magyar Zoltán , Sebestyén Zoltán
Published: December 2010

The theory of noncommutative involutive Banach algebras (briefly Banach *-algebras) owes its origin to Gelfand and Naimark, who proved in 1943 the fundamental representation theorem that a Banach *-algebra with C*-condition

(C*)

is *-isomorphic and isometric to a norm-closed self-adjoint subalgebra of all bounded operators on a suitable Hilbert space.

At the same time they conjectured that the C*-condition can be replaced by the B*-condition.

(B*)

In other words any B*-algebra is actually a C*-algebra. This was shown by Glimm and Kadison [5] in 1960.
Generalized L(f) Spaces
Authors: Hussein D. , Natsheh M. A. , Qumsiyeh I.
Published: December 2010

Given any set Γ, let be the family of all finite subsets of . Let f:[0, ∞) → R satisfying: (1) f(x) = 0 if and only if x = 0, (2) f is increasing, (3) f(x + y) ≧ f(x) + f(y) for all x, y ≦ 0, and (4) f is continuous at zero from the right. Such an f is called a modules. Let C be the set of all moduli, and F = {fv ∊ C:v ∊ Γ). Q(Γ) will denote the set of all such F, s. For each F ∊ Q(Γ) let

the summation is taken over Γ, and set

If Γ is countable Q(Γ) will be denoted by Q and LΓ(F) by L(F). Let

Note that

see [4, 5 and 6].
Strongs-Sequences and Variations on Martin's Axiom
Authors: Steprāns Juris
Published: December 2010

As part of their study of βω — ω and βω1 — ω1, A. Szymanski and H. X. Zhou [3] were able to exploit the following difference between ω, and ω: ω1, contains uncountably many disjoint sets whereas any uncountable family of subsets of ω is, at best, almost disjoint. To translate this distinction between ω1, and ω to a possible distinction between βω1 — ω1, and βω — ω they used the fact that if a pairwise disjoint family of sets and a subset of each member of is chosen then it is trivial to find a single set whose intersection with each member is the chosen set. However, they noticed, it is not clear that the same is true if is only a pairwise almost disjoint family even if we only require equality except on a finite set. But any homeomorphism from βω1 — ω1 to βω — ω would have to carry a disjoint family of subsets of ω1, to an almost disjoint family of subsets of ω with this property. This observation should motivate the following definition.
The Dirichlet Problem for the Subelliptic Laplacian on the Heisenberg Group II
Authors: Gaveau Bernard , Vauthier Jacques
Published: December 2010

Let H3 be the Heisenberg group in three dimensions, Δ the fundamental subelliptic laplacian on H3 (see Section 1 for notations and definitions) and U be an open subset of H3 If φ is a continuous function on the boundary ∂U of U, the Dirichlet problem is thus,

(1)

In [3], p. 104, it was asserted by the first author that, when dU is regular (see Section 1 for this definition), the problem (1) has a solution continuous on D and a probabilistic formula was given. In [3], we prove that our probabilistic formula gives a solution of the so called “martingale problem” associated to Δ on U (see [5] for this notion). But it appears that the connection between the solution in the martingale problem sense and the true solution is not at all clear in the subelliptic case; in particular it is not obvious at all that the probabilistic formula is a C2 function.
A Note on the mod 2 Cohomology of BŜOn〈l6〉
Authors: Ng Tze-Beng
Published: December 2010

Recall BSOn is the classifying space for the special orthogonal group of rank n. It is well known that the mod 2 cohomology ring of BSOn is given as follows:

where wi is the i-th mod 2 Stiefel-Whitney class. For the 3-connective cover of BSOn, BSpinn, Quillen in [4] has determined H*(BSpinn) completely for all n. Let BŜOn〈8〉, BŜOn〈16〉 be the classifying spaces for n-plane spin bundle ξ satisfying w4(ξ) = 0 and w4(ξ) = w8(ξ) = 0 respectively. This note follows the method of A. Borel [2] and gives the mod 2 cohomology ring of BŜOn〈8〉 and BŜOn〈16〉 for small n. In particular we answer the question “when is H*(BŜOn〈8〉; Z2), or H*(BŜOn〈16〉; Z2) a polynomial algebra?”
Corner Behavior of Solutions of Semilinear Dirichlet Problems
Authors: Wigley Neil M.
Published: December 2010

In recent years there has been considerable attention paid to the behavior of solutions of elliptic boundary value problems in domains with piecewise smooth boundary. In two dimensions the study concerns the behavior of a solution near a corner, and in three (or more) dimensions two cases have been given considerable attention: a conical vertex on the boundary, or an edge.

The solution of such a problem may be singular at the nonsmooth boundary points. The standard example in two dimensions is a solution in polar coordinates of the Dirichlet problem near a corner of interior angle πα;u = r1/α sin θ/α is a function which is harmonic in the sector 0 < θ < πα, has zero boundary values near the corner, and yet at the origin has unbounded derivatives of order > 1/α unless 1/α is an integer.
Automorphisms of G-Azumaya Algebras
Authors: Beattie Margaret
Published: December 2010

Let R be a commutative ring, G a finite abelian group of order n and exponent m, and assume n is a unit in R. In [10], F. W. Long defined a generalized Brauer group, BD(R, G), of algebras with a G-action and G-grading, whose elements are equivalence classes of G-Azumaya algebras. In this paper we investigate the automorphisms of a G-Azumaya algebra A and prove that if Picm(R) is trivial, then these automorphisms are all, in some sense, inner.

In fact, each of these “inner” automorphisms can be written as the composition of an inner automorphism in the usual sense and a “linear“ automorphism, i.e., an automorphism of the type

with r(σ) a unit in R. We then use these results to show that the group of gradings of the centre of a G-Azumaya algebra A is a direct summand of G, and thus if G is cyclic of order pr, A is the (smash) product of a commutative and a central G-Azumaya algebra.
A Note on the Multiplicity of Cohen-Macaulay Algebras with Pure Resolutions
Authors: Huneke Craig , Miller Matthew
Published: December 2010

Let R = k[X1, …, Xn] with k a field, and let I ⊂ R be a homogeneous ideal. The algebra R/I is said to have a pure resolution if its homogeneous minimal resolution has the form

Some of the known examples of pure resolutions include the coordinate rings of: the tangent cone of a minimally elliptic singularity or a rational surface singularity [15], a variety defined by generic maximal Pfaffians [2], a variety defined by maximal minors of a generic matrix [3], a variety defined by the submaximal minors of a generic square matrix [6], and certain of the Segre-Veronese varieties [1].

If I is in addition Cohen-Macaulay, then Herzog and Kühl have shown that the betti numbers bi are completely determined by the twists di.
Partitioning Projective Geometries into Caps
Authors: Ebert Gary L.
Published: December 2010

In [2] by means of a fairly lengthy argument involving Hermitian varieties it was shown that PG(2n, q2) can be partitioned into (q2n++ 1 + 1)/(q + l)-caps. Moreover, these caps were shown to constitute the “large points” of a PG(2n, q) in a natural way. In [3] a similar argument was used to show that once two disjoint (n – l)-subspaces are removed from PG(2n, q2), the remaining points can be partitioned into (q2n – 1)/(q2 – l)-caps.

The purpose of this paper is to give a short proof of the results found in [2], and then use the technique developed to partition PG(2n, q) into (qn + l)-caps for n even and q any prime-power. Moreover, these caps can be treated in a natural way as the “large points” of a PG(n – 1, q).
Estimates for Solutions of Wave Equations with Vanishing Curvature
Authors: Marshall Bernard
Published: December 2010

The solution of the Cauchy problem for a hyperbolic partial differential equation leads to a linear combination of operators Tt of the form

For example, the solution of the initial value problem

is given by u(x, t) = Ttf(x) where

Peral proved in [11] that Tt is bounded from LP(Rn) to LP(Rn) if and only if

From the homogeneity, the operator norm satisfies ‖Tt‖ ≦ Ct for all t > 0.
Convexity Conditions on f-Rings
Authors: Larson Suzanne
Published: December 2010

Let n be a positive integer. An f-ring A is said to satisfy the left nth-convexity property if for any u, v ∊ A such that v ≧ 0 and 0 ≧ u ≧ vn, there exists a w ∊ A such that u = wv. The right nth-convexity property is defined similarly and an f-ring is said to satisfy the nth-convexity property if it satisfies both the left and the right nth-convexity property. In this paper, we study arbitrary f-rings which satisfy one of the convexity properties.

Those f-rings which satisfy one or more of these properties have been studied by several authors. In [3, 1D], L. Gillman and M. Jerison note that any C(X) satisfies the nth-convexity property for all n ≧ 2, and in [3, 14.25], they give several properties that in C(X) are equivalent to the 1st-convexity property. M. Henriksen proves some results about the ideal theory of an f-ring satisfying the 2nd-convexity property in [5] and S. Steinberg studies left quotient rings of f-rings satisfying the left 1st-convexity property in [13].
q-Series Identities and Reducibility of Basic Double Hypergeometric Functions
Authors: Srivastava H. M. , Jain V. K.
Published: December 2010

For real or complex q, |q| < 1, let

(1.1)

for arbitrary λ and μ, so that

(1.2)

and

(1.3)

Define, as usual, a generalized q-hypergeometric function by (cf. [26, Chapter 3]; see also [18])

(1.4)

where, for convergence, |q| < 1 and |z| < ∞ when r is a positive integer, or |z| < 1 when r = 0, provided that no zeros appear in the denominator.
The Fourier Transforms of Smooth Measures on Hypersurfaces of Rn + 1
Authors: Marshall Bernard
Published: December 2010

The Fourier transform of the surface measure on the unit sphere in Rn + 1, as is well-known, equals the Bessel function

Its behaviour at infinity is described by an asymptotic expansion

The purpose of this paper is to obtain such an expression for surfaces Σ other than the unit sphere. If the surface Σ is a sufficiently smooth compact n-surface in Rn + 1 with strictly positive Gaussian curvature everywhere then with only minor changes in the main term, such an asymptotic expansion exists. This result was proved by E. Hlawka in [3]. A similar result concerned with the minimal smoothness of Σ was later obtained by C. Herz [2].
A Trace Condition Equivalent to Simultaneous Triangularizability
Authors: Radjavi Heydar
Published: December 2010

A collection of matrices over a field F is said to be triangularizable if there is an invertible matrix T over F such that the matrices T−1ST, are all upper triangular. It is a well-known and easy fact that any commutative set is triangularizable if F is algebraically closed, or if F contains the spectrum of every member of . Many sufficient conditions are known for triangularizability of matrix collections. Levitzki [7] proved that a (multiplicative) semigroup of nilpotent matrices is triangularizable. (His result is valid even over a division ring.) Kolchin [5] showed the triangularizability of a semigroup of unipotent matrices, i.e., matrices of the form I + N with N nilpotent. Kaplansky [3, 4] unified and generalized these results.
On Sieved Orthogonal Polynomials II: Random Walk Polynomials
Authors: Charris Jairo , Ismail Mourad E. H.
Published: December 2010

A birth and death process is a stationary Markov process whose states are the nonnegative integers and the transition probabilities

(1.1)

satisfy

(1.2)

as t → 0. Here we assume βn > 0, δn + 1 > 0, n = 0, 1, …, but δ0 ≦ 0. Karlin and McGregor [10], [11], [12], showed that each birth and death process gives rise to two sets of orthogonal polynomials. The first is the set of birth and death process polynomials {Qn(x)} generated by
On Cesàro and Abel Summability Factors for Integrals
Authors: Borwein David , Thorpe Brian
Published: December 2010

Many results have been obtained about factors transforming integrals summable by ordinary and absolute Cesàro methods of non-negative orders into integrals summable by such methods (see [4], [2], [6], [3]) and also into integrals summable by the ordinary and absolute Abel methods (see [7]). Since the Cesàro summability methods (C, α) and |C, α| for integrals are defined for α ≦ –1, it is natural to try to extend the above mentioned results for α ≦ 0 to the case –1 ≧ α < 0. In this paper we restrict attention to the simplest case α = –1, and classify the summability factors from (C, –1) and |C, –1| to (C, –1) , |C, –1|, (C, λ), |C, λ|, A and |A|, where λ ≦ 0 and A denotes Abel summability.
Structural Properties of a New Class of CM-Lattices
Authors: Johnson Johnny A. , Sherette Gerald R.
Published: December 2010

1. Introduction. In this paper we introduce and study a class of multiplicative lattices called q-lattices. A q-lattice is a principally generated multiplicative lattice in which each principal element is compact. One of our main objectives is to characterize principal elements in these lattices (We note that Noether lattices and r-lattices are q-lattices [1, Theorem 2.1] and so our results apply to these two types of lattices). Among other things we determine necessary and sufficient conditions for globalizing local results in q-lattices. We then apply localization to establish some properties of principal elements in general q-lattices. Conditions equivalent to an element being principal are known for several different classes of multiplicative lattices. For example, Bogart [2] showed that if the lattice is modular, weak principal is equivalent to principal; Johnson and Lediaev pointed out that for Noether lattices, meet principal is equivalent to principal [5]; and, in an r-lattice, an element is principal if and only if it is compact and weak meet principal [6].
Tensor Products of Dimension Groups and K0 of Unit-Regular Rings
Authors: Goodearl K. R. , Handelman D. E.
Published: December 2010

We study direct limits of finite products of matrix algebras (i.e., locally matricial algebras), their ordered Grothendieck groups (K0), and their tensor products. Given a dimension group G, a general problem is to determine whether G arises as K0 of a unit-regular ring or even as K0 of a locally matricial algebra. If G is countable, this is well known to be true. Here we provide positive answers in case (a) the cardinality of G is ℵ1, or (b) G is an arbitrary infinite tensor product of the groups considered in (a), or (c) G is the group of all continuous real-valued functions on an arbitrary compact Hausdorff space. In cases (a) and (b), we show that G in fact appears as K0 of a locally matricial algebra. Result (a) is the basis for an example due to de la Harpe and Skandalis of the failure of a determinantal property in a non-separable AF C*-algebra [18, Section 3].