Recently, there has been a growing interest in understanding the complexity of common analytic equivalence relations between separable Banach spaces via the notion of Borel reducibility in descriptive set theory (see [Bos] [FG] [FLR] [FR1] [FR2] [Me]). In general, the notion of Borel reducibility yields a hierarchy (though not linear) among equivalence relations in terms of their relative compl...

M. Gromov [8] suggested to use uniform embeddings into a Hilbert space or into a uniformly convex space as a tool for solving some of the well-known problems. G. Yu [20] and G. Kasparov and G. Yu [10] have shown that this is indeed a very powerful tool. G. Yu in [20] used the condition of embeddability into a Hilbert space; G. Kasparov and G. Yu [10] used the condition of embeddability into a g...

The present thesis deals with computable functional analysis and in this context, especially, with compact operators on computable Banach spaces. For this purpose, the representation based approach to computable analysis (TTE) is used. In the first part, computable Banach spaces with computable Schauder bases are introduced and two representations each are defined for the dual space of a comput...

We investigate the existence of infinite dimensional Banach spaces having rigid sets with an infinite number of elements. Among Banach lattices, examples are provided by infinite dimensional AM -spaces as well as for some abstract Lp-spaces, 1 ≤ p < ∞.

Type and cotype are computed for Banach spaces generated by some positive sublinear operators and Banach function spaces. Applications of the results yield that under certain assumptions Clarkson’s inequalities hold in these spaces.

Abstract. We introduce stronger versions of the usual notions of martingale type p ≤ 2 and cotype q ≥ 2 of a Banach space X and show that these concepts are equivalent to uniform p-smoothness and q-convexity, respectively. All these are metric concepts, so they depend on the particular norm in X. These concepts allow us to get some more insight into the fine line between X being isomorphic to a...

the purpose of this paper is to study and give the necessary andsufficient condition of strong convergence of the multi-step iterative algorithmwith errors for a finite family of generalized asymptotically quasi-nonexpansivemappings to converge to common fixed points in banach spaces. our resultsextend and improve some recent results in the literature (see, e.g. [2, 3, 5, 6, 7, 8,11, 14, 19]).

1. Compact operators on Banach spaces 2. Appendix: total boundedness and Arzela-Ascoli [Fredholm 1900/1903] treated compact operators as limiting cases of finite-rank operators. [1] [Riesz 1917] defined and made direct use of the compactness condition, more apt for Banach spaces. See [Riesz-Nagy 1952] for extensive discussion in the Hilbert-space situation, and many references to original paper...

For every n ≥ 3, we construct an n-dimensional Banach space which is isometric to a subspace of L1/2 but is not isometric to a subspace of L1. The isomorphic version of this problem (posed by S. Kwapien in 1969) is still open. Another example gives a Banach subspace of L1/4 which does not embed isometrically in L1/2. Note that, from the isomorphic point of view, all the spaces Lq with q < 1 hav...