bluuebunny/crossref_metadata_2025_split huggingface dataset:
Dual functors and the Radon-Nikodym property in the category of Banach spaces
Authors: Pelletier John Wick 
Published: April 2009

AbstractThe notion of duality of functors is used to study and characterize spaces satisfying the Radon-Nikodym property. A theorem of equivalences concerning the Radon-Nikodym property is proved by categorical means; the classical Dunford-Pettis theorem is then deduced using an adjointness argument. The functorial properties of integral operators, compact operators, and weakly compact operators are discussed. It is shown that as an instance of Kan extension the weakly compact operators can be expressed as a certain direct limit of ordinary hom functors. Characterizations of spaces satisfying the Radon-Nikodym property are then given in terms of the agreement of dual functors of the functors mentioned above.
The type set of a torsion-free abelian group of rank two
Authors: Jackett David R. 
Published: April 2009

AbstractIn this paper we generalize a recent result of Freedman (1973) concerning the cardinality of the type set of a rank two torsion-free abelian group. We show that ifAis such a group andAsupports a non-trivial associative ring then the type set ofAcontains at most three elements.
Optimal natural dualities: the role of endomorphisms
Authors: Saramago M. J. 
Published: April 2009

AbstractThe optimality of dualities on a quasivariety , generated by a finite algebra , has been introduced by Davey and Priestley in the 1990s. Since every optimal duality is determined by a transversal of a certain family of subsets of Ω, where Ω is a given set of relations yielding a duality on , an understanding of the structures of these subsets—known as globally minimal failsets—was required. A complete description of globally minimal failsets which do not contain partial endomorphisms has recently been given by the author and H. A. Priestley. Here we are concerned with globally minimal failsets containing endomorphisms. We aim to explain what seems to be a pattern in the way endomorphisms belong to these failsets. This paper also gives a complete description of globally minimal failsets whose minimal elements are automorphisms, when is a subdirectly irreducible lattice-structured algebra.
Operator algebras with a reduction property
Authors: Gifford James A. 
Published: April 2009

AbstractGiven a representation θ: A → B(H) of a Banach algebra A on a Hilbert space H, H is said to have the reduction property as an A—module if every closed invariant subspace of H is complemented by a closed invariant subspace; A has the total reduction property if for every representation θ: A → B(H), H has the reduction property.We show that a C*—algebra has the total reduction property if and only if all its representations are similar to *—representations. The question of whether all C*-algebras have this property is the famous ‘similarity problem’ of Kadison.We conjecture that non-self-adjoint operator algebras with the total reduction property are always isomorphic to C*-algebras, and prove this result for operator algebras consisting of compact operators.
Class preserving automorphisms of Blackburn groups
Authors: Herman Allen , Li Yuanlin 
Published: April 2009

AbstractIn this article, a Blackburn group refers to a finite non-Dedekind group for which the intersection of all nonnormal subgroups is not the trivial subgroup. By completing the arguments of M. Hertweck, we show that all conjugacy class preserving automorphisms of Blackburn groups are inner automorphisms.
Elements of rings and Banach algebras with related spectral idempotents
Authors: Castro-González N. , Vélez-Cerrada J. Y. 
Published: April 2009

AbstractLet aπ denote the spectral idempotent of a generalized Drazin invertible element a of a ring. We characterize elements b such that 1 − (bπ − aπ)2 is invertible. We also apply this result in rings with involution to obtain a characterization of the perturbation of EP elements. In Banach algebras we obtain a characterization in terms of matrix representations and derive error bounds for the perturbation of the Drazin Inverse. This work extends recent results for matrices given by the same authors to the setting of rings and Banach algebras. Finally, we characterize generalized Drazin invertible operators A, B ∈ (X) such that pr(Bπ) = pr(Aπ + S), where pr is the natural homomorphism of (X) onto the Calkin algebra and S ∈(X) is given.2000 Mathematics subject classification: primary 16A32, 16A28, 15A09.
Growth properties and sequences of zeros of analytic functions in spaces of Dirichlet type
Authors: Girela Daniel , Peláez José Ángel 
Published: April 2009

AbstractFor 0 < p < ∞, we let pp−1 denote the space of those functions f that are analytic in the unit disc Δ = {z ∈ C: |z| < 1} and satisfy ∫Δ(1 – |z|)p−1|f′(z)|pdx dy < ∞ The spaces pp−1 are closely related to Hardy spaces. We have, p−1p ⊂ Hp, if 0 < p ≦ 2, and Hp ⊂ pp−1, if 2 ≦ p < ∞. In this paper we obtain a number of results about the Taylor coefficients of pp-1 -functions and sharp estimates on the growth of the integral means and the radial growth of these functions as well as information on their zero sets.2000 Mathematics subject classification: primary 30D35, 30D55, 46E15.
Resolution in hölder spaces of an elliptic problem in an unbounded domain
Authors: Berroug Tarik , Labbas Rabah , Sadallah Boubaker-Khaled 
Published: April 2009

AbstractIn this paper we give new results concerning the maximal regularity of the strict solution of an abstract second-order differential equation, with non-homogeneous boundary conditions of Dirichlet type, and set in an unbounded interval. The right-hand term of the equation is a Hölder continuous function.
The factorial moments of additive functions with rational argument
Authors: Šiaulys J. , Stepanauskas G. 
Published: April 2009

AbstractWe consider the weak convergence of the set of strongly additive functions f(q) with rational argument q. It is assumed that f(p) and f(1/p) ∈ {0, 1} for all primes. We obtain necessary and sufficient conditions of the convergence to the limit distribution. The proof is based on the method of factorial moments. Sieve results, and Halász's and Ruzsa's inequalities are used. We present a few examples of application of the given results to some sets of fractions.
Fixed Point Free Actions of Groups of Exponent 5
Authors: Jabara Enrico 
Published: April 2009

AbstractIn this paper we prove that if V is a vector space over a field of positive characteristric p ≠ 5 then any regular subgroup A of exponent 5 of GL(V) is cyclic. As a consequence a conjecture of Gupta and Mazurov is proved to be true.
The unreasonable effectualness of continued function expansions
Authors: Martin Greg 
Published: April 2009

AbstractMany generalizations of continued fractions, where the reciprocal function has been replaced by a more general function, have been studied, and it is often asked whether such generalized expansions can have nice properties. For instance, we might ask that algebraic numbers of a given degree have periodic expansions, just as quadratic irrationals have periodic continued fractions; or we might ask that familiar transcendental constants such as e or π have periodic or terminating expansions. In this paper, we show that there exist such generalized continued function expansions with essentially any desired behaviour.
The strong closure of Boolean algebras of projections in Banach spaces
Authors: Diestel J. , Ricker W. J. 
Published: April 2009

AbstractThis note improves two previous results of the second author. They turn out to be special cases of our main theorem which states: A Banach space X has the property that the strong closure of every abstractly σ-complete Boolean algebra of projections in X is Bade complete if and only if X does not contain a copy of the sequence space ℓ∞.
Certain relations between p-regular class sizes and the p-structure of p-solvable groups
Authors: Beltrán Antonio , Felipe María José 
Published: April 2009

AbstractLet G be a finite p-solvable group for a fixed prime p. We study how certain arithmetical conditions on the set of p-regular conjugacy class sizes of G influence the p-structure of G. In particular, the structure of the p-complements of G is described when this set is {1, m, n} for arbitrary coprime integers m, n > 1. The structure of G is determined when the noncentral p-regular class lengths are consecutive numbers and when all of them are prime powers.
The structure of groups whose subgroups are permutable-by-finite
Authors: De Falco M. , De Giovanni F. , Musella C. , Sysak Y. P. 
Published: April 2009

AbstractA subgroup H of a group G is said to be permutable if HX = XH for each subgroup X of G, and the group G is called quasihamiltonian if all its subgroups are permutable. We shall say that G is a Q F-group if every subgroup H of G contains a subgroup K of finite index which is permutable in G. It is proved that every locally finite Q F-group contains a quasihamiltonian subgroup of finite index. In the proof of this result we use a theorem by Buckley, Lennox, Neumann, Smith and Wiegold concerning the corresponding problem when permutable subgroups are replaced by normal subgroups: if G is a locally finite group such that H/HG is finite for every subgroup H, then G contains an abelian subgroup of finite index.
Polyhedral convex cones and the equational theory of the bicyclic semigroup
Authors: Pastijn F. 
Published: April 2009

AbstractTo any given balanced semigroup identityU≈Wa number of polyhedral convex cones are associated. In this setting an algorithm is proposed which determines whether the given identity is satisfied in the bicylic semigroupor in the semigroup. The semigroupsBCandEdeserve our attention because a semigroup variety contains a simple semigroup which is not completely simple (respectively, which is idempotent free) if and only if this variety containsBC(respectively,E). Therefore, for a given identityU≈Wit is decidable whether or not the variety determined byU≈Wcontains a simple semigroup which is not completely simple (respectively, which is idempotent free).
Expansion and dimension
Authors: Mancuso Vincent J. 
Published: April 2009

AbstractIf (X, τ) is a topological space, is a family of subsets of X, then the expansion of τ by is the topology τ() on X having τ ∪ as a subbase. If (X, τ) has property , when does (X, τ()) have property ? In this paper we answer this question for the property of dimension. We apply our techniques to first countability and related properties.
On lattice-ordered rings in which the square of every element is positive
Authors: Steinberg Stuart A. 
Published: April 2009

AbstractIt is shown that a unital lattice-ordered ring in which the square of every element is positive is embeddable in a product of totally ordered rings provided it is archimedean, semiperfect, or π-regular. Also, some canonical examples of unital l-domains with squares positive that are not totally ordered are discussed.
A maximum principle
Authors: Ng Kung-Fu 
Published: April 2009

AbstractLet K be a nonempty compact set in a Hausdorff locally convex space, and F a nonempty family of upper semicontinuous convex-like functions from K into [–∞, ∞). K is partially ordered by F in a natural manner. It is shown among other things that each isotone, upper semicontinuous and convex-like function g: K → [ – ∞, ∞) attains its K-maximum at some extreme point of K which is also a maximal element of K.Subject classification (Amer. Math. Soc. (MOS) 1970): primary 46 A 40.
On groups of finite height
Authors: Pride Stephen J. 
Published: April 2009

AbstractIn a previous paper, ‘The concept of “largeness” in group theory’, a partial order was defined on the class of infinite groups, and this partial order was seen to give some precision to our intuitive notions of what it means for one infinite group to be ‘larger’ than another. The aim of this paper is to look more closely at groups which are ‘low down’ in this partial order, and to examine the interplay between properties of groups and finiteness conditions in group theory.Subject classification (Amer. Math. Soc. (MOS) 1970): primary 20 E 15, 20 F 15, 20 K 10, 20 K 25; secondary 20 E 10.
Some covering and embedding theorems for inverse semigroups
Authors: McAllister D. B. 
Published: April 2009

AbstractAn inverse semigroupSis calledE-unitary if the equationsea = e = e2together implya2=a. In a previous paper the author showed that every inverse semigroup is an idempotent separating homomorphic image of anE-unitary inverse semigroup. The main question considered in this paper is the following. Given an inverse semigroupSgive a method for constructingE-unitary inverse semigroupsPand idempotent separating homomorphisms φP→Sin such a way that the structure ofPas aP-semigroup is evident.
Graphs With Stability Index One
Authors: Holton D. A. , Sims J. A. 
Published: April 2009

AbstractWe consider the effect on the stability properties of a graph G, of the presence in the automorphism group of G of automorphisms (uv)h, where u and v are vertices of G, and h is a permutation of vertices of G excluding u and v. We find sufficient conditions for an arbitrary graph and a cartesian product to have stability index one, and conjecture in the latter case that they are necessary. Finally we exhibit explicitly a large class of graphs which have stability index one.
Multiplicities in Hayman's alternative
Authors: Bergwelier Walter , Langley J. K. 
Published: April 2009

AbstractIn 1959 Hayman proved an inequality from which it follows that if f is transcendental and meromorphic in the plane then either f takes every finite complex value infinitely often or each derivative f(k), k ≥1, takes every finite non-zero value infinitely often. We investigate the extent to which these values may be ramified, and we establish a generalization of Hayman's inequality in which multiplicities are not taken into account.
Characterizations of collectively precompact and semi-precompact opterators on topological vector spaces
Authors: Deshpande M. V. , Padhye S. M. 
Published: April 2009

AbstractCharacterizations of collectively precompact and collectively semi-precompact sets of operators on topological vector spaces are obtained. These lead to the characterization of totally bounded sets of semi-precompact operators on locally convex spaces.1980 Mathematics subject classification (Amer. Math. Soc): primary 47 B 05, 47 D 15; secondary 46 A 05, 46 A 15.
Differentiability and local rotundity
Authors: Yorke A. C. 
Published: April 2009

AbstractThe concept of very weak local uniform rotundity (very WLUR) is introduced. It is shown that if a Banach space E is WLUR, very WLUR, or LUR then its dual E* is smooth, very smooth, or Fréchet differentiable, respectively, on a norm dense subset. This leads to examples of nonreflexive spaces which are Fréchet differentiable at every nonzero point of a (relatively) norm dense subset of the embedding of E** in the fourth dual. When E is reflexive, necessary and sufficient conditions for E and E* to be WLUR and LUR are given.Subject classification (Amer. Math. Soc. (MOS) 1970): 46 B 99.
Inverse semigroups determined by their partial automorphism monoids
Authors: Goberstein Simon M. 
Published: April 2009

AbstractThe partial automorphism monoid of an inverse semigroup is an inverse monoid consisting of all isomorphisms between its inverse subsemigroups. We prove that a tightly connected fundamental inverse semigroup S with no isolated nontrivial subgroups is lattice determined ‘modulo semilattices’ and if T is an inverse semigroup whose partial automorphism monoid is isomorphic to that of S, then either S and T are isomorphic or they are dually isomorphic chains relative to the natural partial order; a similar result holds if T is any semigroup and the inverse monoids consisting of all isomorphisms between subsemigroups of S and T, respectively, are isomorphic. Moreover, for these results to hold, the conditions that S be tightly connected and have no isolated nontrivial subgroups are essential.
The palindromic width of a free product of groups
Authors: Bardakov Valery , Tolstykh Vladimir 
Published: April 2009

AbstractPalindromes are those reduced words of free products of groups that coincide with their reverse words. We prove that a free product of groups G has infinite palindromic width, provided that G is not the free product of two cyclic groups of order two (Theorem 2.4). This means that there is no uniform bound k such that every element of G is a product of at most k palindromes. Earlier, the similar fact was established for non-abelian free groups. The proof of Theorem 2.4 makes use of the ideas by Rhemtulla developed for the study of the widths of verbal subgroups of free products.
On the square root of the centre of the Hecke algebra of type A
Authors: Francis Andrew , Jones Lenny 
Published: April 2009

AbstractIn this paper we investigate non-central elements of the Iwahori-Hecke algebra of the symmetric group whose squares are central. In particular, we describe a commutative subalgebra generated by certain non-central square roots of central elements, and the generic existence of a rank-three submodule of the Hecke algebra contained in the square root of the centre, but not in the centre. The generators for this commutative subalgebra include the longest word and elements related to trivial and sign characters of the Hecke algebra. We find elegant expressions for the squares of such generators in terms of both the minimal basis of the centre and the elementary symmetric functions of Murphy elements.
On the module structure of a group action on a Lie algebra
Authors: Papistas Athanassios I. 
Published: April 2009

AbstractLet G be a finite group, K a field, and V a finite-dimensional K G-module. Write L(V) for the free Lie algebra on V; similarly, let M ( V) be the free metabelian Lie algebra. The action of G extends naturally to these algebras, so they become KG-modules, which are direct sums of finite-dimensional submodules. This paper explores whether indecomposable direct summands of such a KG-module (for some specific choices of G, K and V) must fall into finitely many isomorphism classes. Of course this is not a question unless there exist infinitely many isomorphism classes of indecomposable KG-modules (that is, K has positive characteristic p and the Sylow p-subgroups of G are non-cyclic) and dim V > 1.The first two results show that the answer is positive for M(V) when K is finite and dim V = 2, but negative when G is the Klein four-group, the characteristic of K is 2, and V is the unique 3-dimnsional submodule of the regular module D. In the third result, G is again the Klein four-group, K is any field of charateristic 2 with more than 2 elements, V is any faithfull module of dimension 2, and B is the unique 3-dimensional quotient of D; the answer is positive for L(V) if and only if it is positive for each of L(B), L(D), and L(V ⊗ V).
On the accuracy of bootstrapping sample quantiles of strongly mixing sequences
Authors: Sun Shuxia 
Published: April 2009

AbstractIn this paper, we examine the rate of convergence of moving block bootstrap (MBB) approximations to the distributions of normalized sample quantiles based on strongly mixing observations. Under suitable smoothness and regularity conditions on the one-dimensional marginal distribution function, the rate of convergence of the MBB approximations to distributions of centered and scaled sample quantiles is of order O(n−1¼ log logn).
Derivative-free characterizations of Qk spaces
Authors: Wulan Hasi , Zhu Kehe 
Published: April 2009

AbstractWe give two charaterizations of the Möbius invariant QK spaces, one in terms of a double integral and the other in terms of the mean oscillation in the Bergman metric. Both charaterizations avoid the use of derivatives. Our results are new even in the case of Qp.
Generalized Ramsey theory VI: Ramsey numbers for small plexes
Authors: Duke Richard A. , Harary Frandk 
Published: April 2009

AbstractGeneralized Ramsey theory for graphs was formulated and developed in the previous papers in this series. We extend the area here by introducing generalized Ramsey numbers for higher dimensional simplicial complexes. In particular we calculate explicitly the Ramsey numbers for several small “pure 2-complexes”, or more brieflyplexes, in which each edge is contained in some 2–call.
A note on polyhedral cones
Authors: Tam Bit-Shun 
Published: April 2009

AbstractIn this short note, two results on a solid, pointed, closed cone C in Rn will be given: first, C is polyhedral iff it has a finite number of maximal faces; second, for any face F of C, C* ∩ F┴ is a face of its dual cone C* of dimension n – dim F.
Separation axioms and subcategories of top
Authors: Nakagawa Ryosuke 
Published: April 2009

Abstract(Point, closed subset)-separation axioms and closed subsets separation axioms for topological spaces will be uniformly defined. Then it is shown that a subcategory of TOP is bireflective in TOP if and only if Ob consists of all separated spaces for some (point, closed subset)-separation axiom. A characterization theorem on subcategories of all separated spaces for closed subsets separation axioms is also given by using the category SEP of all separation spaces and the embedding functor G: TOP → SEP. As an application we have that a T1-space is normal if and only if it is embedded in a product space of the unit intervals in SEP.
Classification of totally umbilical submanifolds in symmetric spaces
Authors: Chen Bang-Yen 
Published: April 2009

AbstractA submanifold of a Riemannian manifold is called a totally umbilical submanifold if the second fundamental form is proportional to the first fundamental form. In this paper, we shall prove that there is no totally umbilical submanifold of codimension less than rank M — 1 in any irreducible symmetric space M. Totally umbilical submanifolds of higher codimensions in a symmetric space are also studied. Some classification theorems of such submanifolds are obtained.
Completely semisimple ring semigroups
Authors: Hannah John , Richardson J. S. , Zeleznikow John 
Published: April 2009

AbstractLet R be a ring in which the multiplicative semigroup is completely semisimple. If R has the maximum (respectively, minimum) condition on principal multiplicative ideals. then R is semiprime artinian (respectively, a direct sum of dense rings of finite-rank linear transformations of vector spaces over division rings).
Positive linear operators and the approximation of continuous functions on locally compact abelian groups
Authors: Bloom Walter R. , Sussich Joseph F. 
Published: April 2009

AbstractIn 1953 P. P. Korovkin proved that if (Tn) is a sequence of positive linear operators defined on the space C of continuous real 2π-periodic functions and limn→rTnf = f uniformly for f = 1, cos and sin. then limn→rTnf = f uniformly for all f∈C. We extend this result to spaces of continuous functions defined on a locally compact abelian group G, with the test family {1, cos, sin} replaced by a set of generators of the character group of G.
Slim trees
Authors: Evans Elliott 
Published: April 2009

AbstractA semilattice tree T with 0 is slim if there is a chain C with 0 so that the lattices θ (T) and θ(C) of semilattice congruences are isomorphic. This paper establishes elementary consequences of slimness and uses simple constructive techniques to show certain small trees slim. If T is the union of at most countably many branches, each of which has a maximum or a countable cotinal subset, then T is slim. For trees with enough maximals slimness is equivalent with not having any uncountable anti-chains. If a tree T has a countable cofinal subset then T is slim. Thus finitary trees are slim.
On the uniform convergence of interpolatory polynomials
Authors: Prasad J. 
Published: April 2009

AbstractHere we consider a problem on weighted (0, 2) interpolation. We choose the interpolatory conditions in such a way that we get the polynomial of degree ≤2n−1, satisfying those conditions. Moreover we prove that the sequence of these interpolatory polynomials under certain conditions converges uniformly to a function belonging to the Zygmund class.