On estimates of the generalized Jordan--von Neumann constant of Banach spaces.
On extremal structure of weakly locally compact convex sets in Banach spaces
On extreme points of Orlicz spaces with Orlicz norm.
In the paper we consider a class of Orlicz spaces equipped with the Orlicz norm over a non-negative, complete and sigma-finite measure space (T,Sigma,mu), which covers, among others, Orlicz spaces isomorphic to L-infinite and the interpolation space L1 + L-infinite. We give some necessary conditions for a point x from the unit sphere to be extreme. Applying this characterization, in the case of an atomless measure mu, we find a description of the set of extreme points of L1 + L-infinite which corresponds...
On Gaps Between Bounded Operators
On Gateaux differentiable bump functions
It is shown that the order of Gateaux smoothness of bump functions on a wide class of Banach spaces with unconditional basis is not better than that of Fréchet differentiability. It is proved as well that in the separable case this order for Banach lattices satisfying a lower p-estimate for 1≤ p < 2 can be only slightly better.
On having a countable cover by sets of small local diameter
A characterization of topological spaces admitting a countable cover by sets of small local diameter close in spirit to known characterizations of fragmentability is obtained. It is proved that if X and Y are Hausdorff compacta such that C(X) has an equivalent p-Kadec norm and has a countable cover by sets of small local norm diameter, then has a countable cover by sets of small local norm diameter as well.
On Hilbert-Schmidt spaces
On Incomparability of Banach Spaces.
On incomparability of Banach spaces
Several concepts of incomparability of Banach spaces have been considered in the literature, which allow one to describe some of the properties of the product of two Banach spaces as a juxtaposition of the corresponding properties of the factors. In this paper we study the relations between these concepts of incomparability, survey the main results and applications, and state some open problems.
On incomparability of Banach spaces.
On infinite dimensional uniform smoothness of Banach spaces
An infinite dimensional counterpart of uniform smoothness is studied. It does not imply reflexivity, but we prove that it gives some -type estimates for finite dimensional decompositions, weak Banach-Saks property and the weak fixed point property.
On isomorphisms by orthogonality of a normed space and an inner product space.
On isomorphisms of spaces of analytic functions onto .
On James and Jordan-von Neumann constants and the normal structure coefficient of Banach spaces
Some relations between the James (or non-square) constant J(X) and the Jordan-von Neumann constant , and the normal structure coefficient N(X) of Banach spaces X are investigated. Relations between J(X) and J(X*) are given as an answer to a problem of Gao and Lau [16]. Connections between and J(X) are also shown. The normal structure coefficient of a Banach space is estimated by the -constant, which implies that a Banach space with -constant less than 5/4 has the fixed point property.
On -nearly uniform convex property in generalized Cesàro sequence spaces.
On K-nearly uniform convexity in Orlicz spaces.
On Kottman's constants in Banach spaces
This paper deals with a few, not widely known, aspects of Kottman's constant of a Banach space and its symmetric and finite variations. We will consider their behaviour under ultrapowers, relations with other parameters such as Whitley's or James' constant, and connection with the extension of c₀-valued Lipschitz maps.
On large subspaces of the Schatten -classes
On local convexity of nonlinear mappings between Banach spaces
We find conditions for a smooth nonlinear map f: U → V between open subsets of Hilbert or Banach spaces to be locally convex in the sense that for some c and each positive ɛ < c the image f(B ɛ(x)) of each ɛ-ball B ɛ(x) ⊂ U is convex. We give a lower bound on c via the second order Lipschitz constant Lip2(f), the Lipschitz-open constant Lipo(f) of f, and the 2-convexity number conv2(X) of the Banach space X.
On mappings, orthogonally additive in the Birkhoff-James sense.