Completeness of quasi-normed symmetric operator spaces

We show that (generalized) Calkin correspondence between quasi-normed symmetric sequence spaces and symmetrically quasi-normed ideals of compact operators on an infinite-dimensional Hilbert space preserves completeness. We also establish a semifinite version of this result.     

Discriminating potentials of measures on certain quasi-normed spaces

A uniqueness theorem for a convolution equation is proved for a class of infinitedimensional spaces larger than the class of Banach spaces, in particular, for L_p-spaces with p > 0.     

Approximate convexity of average sums of sets in normed linear spaces

This note gives a sufficient condition under which the average sum of a large but finite number of sets in an arbitrary normed linear space is approximately convex. The result can be deduced as a simple corollary of an analogous result for a nonstandard universe. The latter has independent interest.     

Complex extreme points and complex convexity in Orlicz-Bochner function spaces

It is well known that extreme points which are connected with strict convexity of the whole spaces, are the most basic and important geometric points in geometric theory of Banach spaces. In this paper, criteria for complex extreme points, complex strict convexity and complex uniform convexity in Orlicz-Bochner function spaces are given.     

Separation properties of convexity spaces

The purpose of this paper is to investigate some separation properties of sets with axiomatically defined convexity structures. We state a general separation theorem for pairs of convexities, improving some known results. As an application, we discuss separation properties of lattices, real vector spaces and modules. Received 21 January 1999.     

The uniform convexity of the Edmunds-Triebel logarithmic spaces

We show how uniform convexity can be preserved in the logarithmic spaces A_θ(logA)_b,p. Estimates are given for the moduli of convexity of A_θ(logA)_b,p in terms of the moduli of A₀ and A₁, when one or both of them are uniformly convex.     

On uniform convexity of Orlicz spaces

In the present paper we present criteria for uniform convexity of Orlicz spaces in the case of a nonatomic measure as well as in the case of a purely atomic measure.     

Uniform convexity of generalized Lorentz spaces

Partially supported by the Fulbright Program.     

关于Banach空间的强凸性

本文讨论强凸性、Ｌ－ｋＲ，ＬωＲ和（Ｇ）性质之间的关系，指出强凸性介于ＬωＲ和（Ｇ）性质之间，证明光滑的有（Ｇ）性质的Ｂａｎａｃｈ空间是强凸的，此外指出存在一个Ｂａｎａｃｈ空间Ｘ，它是ＬωＲ但对任意自然数ｋ，Ｘ不是Ｌ－ｋＲ．     

On uniform convexity of Banach spaces

This paper gives some relations and properties of several kinds of generalized convexity in Banach spaces. As a result, it proves that every kind of uniform convexity implies the Banach-Sakes property, and several notions of uniform convexity in literature are actually equivalent.     

Monodromy of Fuchsian systems on complex linear spaces

On complex linear spaces, Fuchs-type Pfaffian systems are studied that are defined by configurations of vectors in these spaces. These systems are referred to as R-systems in this paper. For the vector configurations that are systems of roots of complex reflection groups, the monodromy representations of R-systems are described. These representations are deformations of the standard representations of reflection groups. Such deformations define representations of generalized braid groups corresponding to complex reflection groups and are similar to the Burau representations of the Artin braid groups.     

On generalized convexity in Asplund spaces

In this paper some properties of nonsmooth quasiconvex and pseudoconvex functions in weakly compactly generated Asplund spaces are proved.     

Uniform convexity in Lorentz sequence spaces

Necessary and sufficient conditions for Lorentz sequence spacesd(a,p) (1<p<∞), to be uniformly convexifiable are given. In casep≧2 the modulus of convexity is calculated.