bluuebunny/crossref_metadata_2025_split huggingface dataset:
Linear Transformations on Symmetric Spaces II
Authors: Lim Ming–Huat 
Published: December 2010

AbstractLet U be a finite dimensional vector space over an infinite field F. Let U(r) denote the r–th symmetric product space over U. Let T: U(r) → U(s) be a linear transformation which sends nonzero decomposable elements to nonzero decomposable elements. Let dim U ≥ s + 1. Then we obtain the structure of T for the following cases: (I) F is algebraically closed, (II) F is the real field, and (III) T is injective.
Conditional Sequence Entropy and Mild Mixing Extensions
Authors: Zhang Qing 
Published: December 2010

AbstractFor a measure preserving system (X, ℬ, μ, T) with a factor (Y, C, v, T) and an infinite sequence {tn}, one can define conditional sequence entropy. We present two theorems which characterize rigid and mildly mixing extensions by conditional sequence entropy. Properties of IP-systems are used to prove our main theorems.
Spectral Integration of Marcinkiewicz Multipliers
Authors: Asmar Nakhlé , Berkson Earl , Gillespie T. A. 
Published: December 2010

AbstractLet X be a closed subspace of LP(μ), where μ is an arbitrary measure and 1 < p < ∞. By extending the scope of spectral integration, we show that every invertible power-bounded linear mapping of X into X has a functional calculus implemented by the algebra of complex-valued functions on the unit circle satisfying the hypotheses of the Strong Marcinkiewicz Multiplier Theorem. This result expands the framework of the Strong Marcinkiewicz Multiplier Theorem to the setting of abstract measure spaces.
On the Ideal of Veronesean Surfaces
Authors: Gimigliano A. , Lorenzini A. 
Published: December 2010

AbstractWe consider the blowing up of ℙ2 at s sufficiently general distinct points and its projective embedding by the linear system of the curves of a given degree through the points. We study the ideal of the resulting (Veronesean) surface and find that it can be described by two matrices of linear forms, in the sense that it is generated by the entries of the product matrix and the minors of complementary orders of the two matrices.By cutting the surface twice with general hyperplanes, we also obtain some information about the generation (or even the resolution) of certain classes of points in projective space.
A Calculus of EPI-Derivatives Applicable to Optimization
Authors: Poliquin R. A. , Rockafellar R. T. 
Published: December 2010

AbstractWhen an optimization problem is represented by its essential objective function, which incorporates constraints through infinite penalties, first- and secondorder conditions for optimality can be stated in terms of the first- and second-order epi-derivatives of that function. Such derivatives also are the key to the formulation of subproblems determining the response of a problem's solution when the data values on which the problem depends are perturbed. It is vital for such reasons to have available a calculus of epi-derivatives. This paper builds on a central case already understood, where the essential objective function is the composite of a convex function and a smooth mapping with certain qualifications, in order to develop differentiation rules covering operations such as addition of functions and a more general form of composition. Classes of "amenable" functions are introduced to mark out territory in which this sharper form of nonsmooth analysis can be carried out.
Covering Games and the Banach-Mazur Game: K-tactics
Authors: Bartoszynski Tomek , Just Winfried , Scheepers Marion 
Published: December 2010

AbstractGiven a free ideal J of subsets of a set X, we consider games where player ONE plays an increasing sequence of elements of the σ-completion of J, and player TWO tries to cover the union of this sequence by playing one set at a time from J. We describe various conditions under which player TWO has a winning strategy that uses only information about the most recent k moves of ONE, and apply some of these results to the Banach-Mazurgame.
On Convex Functions Having Points of Gateaux Differentiability Which are Not Points of Fréchet Differentiability
Authors: Borwein J. M. , Fabian M. 
Published: December 2010

AbstractWe study the relationships between Gateaux, Fréchet and weak Hadamard differentiability of convex functions and of equivalent norms. As a consequence we provide related characterizations of infinite dimensional Banach spaces and of Banach spaces containing ł1. Explicit examples are given. Some renormings of WCG Asplund spaces are made in this vein.
Dense Subgroups of the Automorphism Groups of Free Algebras
Authors: Bryant Roger M. , Drensky Vesselin 
Published: December 2010

AbstractLet F be the free metabelian Lie algebra of finite rank m over a field K of characteristic 0. The automorphism group Aut F is considered with respect to a topology called the formal power series topology and it is shown that the group of tame automorphisms (automorphisms induced from the free Lie algebra of rank m) is dense in Aut F for m ≥ 4 but not dense for m = 2 and m = 3. At a more general level, we study the formal power series topology on the semigroup of all endomorphisms of an arbitrary (associative or non-associative) relatively free algebra of finite rank m and investigate certain associated modules of the general linear group GLm(AT).
A+∞ Condition
Authors: Martín-Reyes F. J. , Pick L. , De La Torre A. 
Published: December 2010

AbstractThe good weights for the one-sided Hardy-Littlewood operators have been characterized by conditions . In this paper we introduce a new condition which is analogous to A∞. We show several characterizations of . For example, we prove that the class of weights is the union of classes. We also give a new characterization of weights. Finally, as an application of condition, we characterize the weights for one-sided fractional integrals and one-sided fractional maximal operators.
Homomorphisms of Distributive Lattices as Restrictions of Congruences. II. Planarity and Automorphisms
Authors: Grätzer G. , Lakser H. 
Published: December 2010

AbstractWe prove that any {0,1 }-preserving homomorphism of finite distributive lattices can be realized as the restriction of the congruence relations of a finite planar lattice with no nontrivial automorphisms to an ideal of that lattice, where this ideal also has no nontrivial automorphisms. We also prove that any {0,1 }-preserving homomorphism of finite distributive lattices with more than one element and any homomorphism of groups can be realized, simultaneously, as the restriction of the congruence relations and, respectively, the restriction of the automorphisms of a lattice L to those of an ideal of L; if the groups are both finite, then so is the lattice L.
Kernel Generated Two-Time Parameter Gaussian Processes and Some of Their Path Properties
Authors: Csörgő Miklós , Lin Zheng-Yan , Shao Qi-Man 
Published: December 2010

AbstractWe study path properties of kernel generated two-time parameter, not necessarily stationary, Gaussian processes. We establish large deviation results for some increments of these processes and use these results to prove some of their moduli of continuity and other path properties.
Operator Algebras with Contractive Approximate Identities
Authors: Poon Yiu-Tung , Ruan Zhong-Jin 
Published: December 2010

AbstractWe study operator algebras with contractive approximate identities and their double centralizer algebras. These operator algebras can be characterized as L∞- Banach algebras with contractive approximate identities. We provide two examples, which show that given a non-unital operator algebra A with a contractive approximate identity, its double centralizer algebra M(A) may admit different operator algebra matrix norms, with which M(A) contains A as an M-ideal. On the other hand, we show that there is a unique operator algebra matrix norm on the unitalization algebra A1 of A such that A1 contains A as an M-ideal.
Invariant Neutral Subspaces for Symmetric and Skew Real Matrix Pairs
Authors: Lancaster P. , Rodman L. 
Published: December 2010

AbstractReal matrix pairs (A,H) satisfying det H ≠ 0, HT = εH, and HA - ηATH, where ε, η take the values +1 or —1, are considered. It is shown that maximal A-invariant H-neutral subspaces have the same dimension (depending on ε and η), called the order of neutrality of the pair (A, H). The order of neutrality of definitizable pairs is investigated. In particular, this concept is used to obtain lower bounds for the number of pure imaginary eigenvalues of low rank perturbations of definitizable pairs when (ε,η) = (1, - 1 ) and when (ε,η) = (—1,—1).
Conjugacy Classes in Algebraic Monoids II
Authors: Putcha Mohan S. 
Published: December 2010

AbstractLet M be a connected linear algebraic monoid with zero and a reductive unit group. We show that there exist reductive groups G1,..., Gt, each with an automorphism, such that the conjugacy classes of M are in a natural bijective correspondence with the twisted conjugacy classes of Gi, i = 1,..., t.
Exact Inequalities for the Norms of Factors of Polynomials
Authors: Borwein Peter B. 
Published: December 2010

AbstractThis paper addresses a number of questions concerning the size of factors of polynomials. Let p be a monic algebraic polynomial of degree n and suppose q1q2 … qi is a monic factor of p of degree m. Then we can, in many cases, exactly determine Here ‖ . ‖ is the supremum norm either on [—1, 1] or on {|z| ≤ 1}. We do this by showing that, in the interval case, for each m and n, the n-th Chebyshev polynomial is extremal. This extends work of Gel'fond, Mahler, Granville, Boyd and others. A number of variants of this problem are also considered.
Simplicity Of Reduced Amalgamated Products of C*-Algebras
Authors: McClanahan Kevin 
Published: December 2010

AbstractWe give sufficient conditions for the simplicity of reduced amalgamated products of C*-algebras. We show that in some situations a minimal projection in a unital C*-algebra A is minimal in a free product A *-cB. We show that in certain situations if a minimal projection in A were minimal in a particular reduced free product of A and B then the reduced free product would be a simple C*-algebra which has finite and infinite projections.
Weakly Purely Finitely Additive Measures
Authors: Rüttimann Gottfried T. 
Published: December 2010

AbstractLet L be an orthomodular poset. A positive measure ξ on L is said to be weakly purely finitely additive if the zero measure is the only completely additive
measure majorized by ξ. It was shown in [15] that, in an arbitrary orthomodular poset L, every positive measures μ is the sum v + ξ of a positive completely additive measure
v and a weakly purely finitely additive measure ξ. We give sufficient conditions for this
Yosida-Hewitt-type decomposition to be unique.A positive measure λ on L is said to be filtering if every non-zero element p in L majorizes a non-zero element q on which λ vanishes. A filtering measure is weakly purely finitely additive. Filtering measures play a mediator role throughout these investigations since some of the aforementioned conditions are given in terms of these.The results obtained here are then viewed in the context of Boolean lattices and applied to lattices of idempotents of non-associative JBW-algebras.
Loops as Invariant Sections in Groups, and their Geometry
Authors: Nagy Péter T. , Strambach Karl 
Published: December 2010

AbstractWe investigate left conjugacy closed loops which can be given by invariant sections in the group generated by their left translations. These loops are generalizations of the conjugacy closed loops introduced in [13] just as Bol loops generalize Moufang loops. The relations of these loops to common classes of loops are studied. For instance on a connected manifold we construct proper topological left conjugacy closed loops satisfying the left Bol condition but show that any differentiable such loop must be a group. We show that the configurational condition in the 3-net corresponding to an isotopy class of left conjugacy closed loops has the same importance in the geometry of 3-nets as the Reidemeister or the Bol condition.
Weighted Lorentz Norm Inequalities for the One-Sided Hardy-Littlewood Maximal Functions and for the Maximal Ergodic Operator
Authors: Ortega Salvador P. 
Published: December 2010

AbstractIn this paper we characterize weighted Lorentz norm inequalities for the one sided Hardy-Littlewood maximal functionSimilar questions are discussed for the maximal operator associated to an invertible measure preserving transformation of a measure space.
The Universal Theory of Ordered Equidecomposability Types Semigroups
Authors: Wehrung Friedrich 
Published: December 2010

AbstractWe prove that a commutative preordered semigroup embeds into the space of all equidecomposability types of subsets of some set equipped with a group action (in short, a full type space) if and only if it satisfies the following axioms: (i) (⩝x,y) (x ≤ x + y); (ii) (⩝x,y)((x ≤ y and y ≤ x) ⇒ x = y); (iii) (⩝x,y,u, v)((x + u ≤ y + u and u ≤ v) ⩝ x + v ≤ y ≤ v); (iv) (⩝x, u, V)((x + u = u and u ≤ v) ⇒ x + v = v); (v) (⩝x,y)(mx ≤ my ⇒ x ≤ y) (all m ∊ Ν \ {0}). Furthermore, such a structure can always be embedded into a reduced power of the space Τ of nonempty initial segments of + with rational (possibly infinite) endpoints, equipped with the addition defined by and the ordering defined by . As a corollary, the set of all universal formulas of (+, ≤) satisfied by all full type spaces is decidable.
Sharpness in Young's Inequality for Convolution Products
Authors: Nielsen Ole A. 
Published: December 2010

AbstractSuppose that Gis a locally compact group with modular function Δ and that p, q, r are three numbers in the interval (l,∞) satisfying. If cp,q(G) is the smallest constant c such thatfor all functions f, g ∈ Cc(G) (here the convolution product is with respect to left Haar measure andis the exponent which is conjugate to p) then Young's inequality asserts that cp,q(G) ≤ 1. This paper contains three results about these constants. Firstly, if G contains a compact open subgroup then cp,q(G) = 1 and, as an extension of an earlier result of J. J. F. Fournier, it is shown that there is a constant cp,q&lt; 1 such that if G does not contain a compact open subgroup then c&lt;(G) ≤ c≤. Secondly, Beckner's calculation ofis used to obtain the value of cp,q(G) for all simply-connected solvable Lie groups and all nilpotent Lie groups. And thirdly, it is shown that for a nilpotent Lie group the setis not contained in the union of the spaces Ls(G),.
Multipliers on Spaces of Analytic Functions
Authors: Blasco Oscar 
Published: December 2010

AbstractIn the paper we find, for certain values of the parameters, the spaces of multipliers (H(p, q, α), H(s, t, β) and (H(p, q, α), ls), where H(p, q, α) denotes the space of analytic functions on the unit disc such that . As corollaries we recover some new results about multipliers on Bergman spaces and Hardy spaces.
On Orthogonal Polynomials With Respect to a Positive Definite Matrix of Measures
Authors: Duran Antonio J. 
Published: December 2010

AbstractIn this paper, we prove that any sequence of polynomials (pn)n for which dgr(pn) = n which satisfies a (2N + l)-term recurrence relation is orthogonal with respect to a positive definite N × N matrix of measures. We use that result to prove asymptotic properties of the kernel polynomials associated to a positive measure or a positive definite matrix of measures. Finally, some examples are given.
The Generalized Wielandt Subgroup of a Group
Authors: Beidleman James C. , Dixon Martyn R. , Robinson Derek J. S. 
Published: December 2010

AbstractThe intersection IW(G) of the normalizers of the infinite subnormal subgroups of a group G is a characteristic subgroup containing the Wielandt subgroup W(G) which we call the generalized Wielandt subgroup. In this paper we show that if G is infinite, then the structure of IW(G)/ W(G) is quite restricted, being controlled by a certain characteristic subgroup S(G). If S(G) is finite, then so is IW(G)/ W(G), whereas if S(G) is an infinite Prüfer-by-finite group, then IW(G)/W(G) is metabelian. In all other cases, IW(G) = W(G).
On the Ergodic Averages and the Ergodic Hilbert Transform
Authors: Fernández-Cabrera L. M. , Martín-Reyes F. J. , Torrea J. L. 
Published: December 2010

AbstractLet T be an invertible measure-preserving transformation on a σ-finite measure space (X, μ) and let 1 < p < ∞. This paper uses an abstract method developed by José Luis Rubio de Francia which allows us to give a unified approach to the problems of characterizing the positive measurable functions v such that the limit of the ergodic averages or the ergodic Hilbert transform exist for all f ∈ Lp(νdμ). As a corollary, we obtain that both problems are equivalent, extending to this setting some results of R. Jajte, I. Berkson, J. Bourgain and A. Gillespie. We do not assume the boundedness of the operator Tf(x) = f(Tx) on Lp(νdμ). However, the method of Rubio de Francia shows that the problems of convergence are equivalent to the existence of some measurable positive function u such that the ergodic maximal operator and the ergodic Hilbert transform are bounded from LP(νdμ) into LP(udμ). We also study and solve the dual problem.
Distance From Projections to Nilpotents
Authors: Macdonald Gordon W. 
Published: December 2010

AbstractThe distance from an arbitrary rank-one projection to the set of nilpotent operators, in the space of k × k matrices with the usual operator norm, is shown to be sec(π/(k:+2))/2. This gives improved bounds for the distance between the set of all non-zero projections and the set of nilpotents in the space of k × k matrices. Another result of note is that the shortest distance between the set of non-zero projections and the set of nilpotents in the space of k × k matrices is .
On Permutability and Submultiplicativity of Spectral Radius
Authors: Longstaff W. E. , Radjavi H. 
Published: December 2010

AbstractLet r(T) denote the spectral radius of the operator T acting on a complex Hilbert space H. Let S be a multiplicative semigroup of operators on H. We say that r is permutable on 𝓢 if r(ABC) = r(BAC), for every A,B,C ∈ 𝓢. We say that r is submultiplicative on 𝓢 if r(AB) ≤ r(A)r(B), for every A, B ∈ 𝓢. It is known that, if r is permutable on 𝓢, then it is submultiplicative. We show that the converse holds in each of the following cases: (i) 𝓢 consists of compact operators (ii) 𝓢 consists of normal operators (iii) 𝓢 is generated by orthogonal projections.
Frames and Stable Bases for Shift-Invariant Subspaces of L2(ℝd)
Authors: Ron Amos , Shen Zuowei 
Published: December 2010

AbstractLet X be a countable fundamental set in a Hilbert space H, and let T be the operator Whenever T is well-defined and bounded, X is said to be a Bessel sequence. If, in addition, ran T is closed, then X is a frame. Finally, a frame whose corresponding T is injective is a stable basis (also known as a Riesz basis). This paper considers the above three properties for subspaces H of L2(ℝd), and for sets X of the form with Φ either a singleton, a finite set, or, more generally, a countable set. The analysis is performed on the Fourier domain, where the two operators TT* and T* T are decomposed into a collection of simpler "fiber" operators. The main theme of the entire analysis is the characterization of each of the above three properties in terms of the analogous property of these simpler operators.
On the Recovery of Analytic Functions
Authors: Cima Joseph A. , Stessin Michael 
Published: December 2010

AbstractIn this paper we consider questions of recapturing an analytic function in a Banach space from its values on a uniqueness set. The principal method is to use reproducing kernels to construct a sequence in the Banach space which converges in norm to the given functions. The method works for several classical Banach spaces of analytic functions including some Hardy and Bergman spaces.
Dade's Conjecture for Chevalley Groups G2(q) in Non-Defining Characteristics
Authors: An Jianbei , Gao Yun 
Published: December 2010

AbstractThis paper is part of a program to study the conjecture of E. C. Dade on counting characters in blocks for several finite groups of Lie type. The local structures of certain radical chains of Chevalley groups of type G2 are given and the ordinary conjecture is confirmed for the groups when the characteristic of the modular representation is distinct from the defining characteristic of the groups.
Necessary and Sufficient Conditions for Mean Convergence of Lagrange Interpolation for Erdős Weights
Authors: Damelin S. B. , Lubinsky D. S. 
Published: December 2010

AbstractWe investigate mean convergence of Lagrange interpolation at the zeros of orthogonal polynomials pn(W2, x) for Erdös weights W2 = e-2Q. The archetypal example is Wk,α = exp(—Qk,α), whereα > 1, k ≥ 1, and is the k-th iterated exponential. Following is our main result: Let 1 < p < ∞, Δ ∊ ℝ, k > 0. Let Ln[f] denote the Lagrange interpolation polynomial to ƒ at the zeros of pn(W2, x) = pn(e-2Q, x). Then forto hold for every continuous function ƒ: ℝ —> ℝ satisfyingit is necessary and sufficient that
First Order Operators on Manifolds With a Group Action
Authors: Fegan H. D. , Steer B. 
Published: December 2010

AbstractWe investigate questions of spectral symmetry for certain first order differential operators acting on sections of bundles over manifolds which have a group action. We show that if the manifold is in fact a group we have simple spectral symmetry for all homogeneous operators. Furthermore if the manifold is not necessarily a group but has a compact Lie group of rank 2 or greater acting on it by isometries with discrete isotropy groups, and let D be a split invariant elliptic first order differential operator, then D has equivariant spectral symmetry.
Forbidden Subcategories of Non-Polynomial Growth Tame Simply Connected Algebras
Authors: De La Peña J. A. , Skowroński A. 
Published: December 2010

AbstractLet k be an algebraically closed field and A = kQ/I be a basic finite dimensional k-algebra such that Q is a connected quiver without oriented cycles. Assume that A is strongly simply connected, that is, for every convex subcategory B of A the first Hochschild cohomology H1(B, B) vanishes. The algebra A is sincere if it admits an indecomposable module having all simples as composition factors. We study the structure of strongly simply connected sincere algebras of tame representation type. We show that a sincere, tame, strongly connected algebra A which contains a convex subcategory which is either representation-infinite tilted of type Ẽp, p = 6,7,8, or a tubular algebra, is of polynomial growth.
Greenberg's Theorem for Quasiconvex Subgroups of Word Hyperbolic Groups
Authors: Kapovich Ilya , Short Hamish 
Published: December 2010

AbstractAnalogues of a theorem of Greenberg about finitely generated subgroups of free groups are proved for quasiconvex subgroups of word hyperbolic groups. It is shown that a quasiconvex subgroup of a word hyperbolic group is a finite index subgroup of only finitely many other subgroups.
The Residual Spectrum ofG2
Authors: Kim Henry H. 
Published: December 2010

AbstractWe completely determine the residual spectrum of the split exceptional group of typeG2, thus completing the work of Langlands and Moeglin-Waldspurger on the part of the residual spectrum attached to the trivial character of the maximal torus. We also give the Arthur parameters for the residual spectrum coming from Borel subgroups. The interpretation in terms of Arthur parameters explains the “bizarre” multiplicity condition in Moeglin-Waldspurger's work. It is related to the fact that the component group of the Arthur parameter is non-abelian.
Compactness of a Locally Compact Group G and Geometric Properties of Ap(G)
Authors: Miao Tianxuan 
Published: December 2010

AbstractLet G be a locally compact topological group. A number of characterizations are given of the class of compact groups in terms of the geometric properties such as Radon-Nikodym property, Dunford-Pettis property and Schur property of Ap(G), and the properties of the multiplication operator on PFp(G). We extend and improve several results of Lau and Ülger [17] to Ap(G) and Bp(G) for arbitrary p.