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The James-Schreier spaces, defined by amalgamating James' quasi-reflexive Banach spaces and Schreier space, can be equipped with a Banach-algebra structure. We answer some questions relating to their cohomology and ideal structure, and investigate the relations between them. In particular we show that the James-Schreier algebras are weakly amenable but not amenable, and relate these algebras to their multiplier algebras and biduals.
We present a simple proof of a Banach-Stone type Theorem. The method used in the proof also provides an answer to a conjecture of Cao, Reilly and Xiong.
Given an operator ideal , we say that a Banach space X has the approximation property with respect to if T belongs to for every Banach space Y and every T ∈ (Y,X), being the topology of uniform convergence on compact sets. We present several characterizations of this type of approximation property. It is shown that some of the existing approximation properties in the literature may be included in this setting.
Inspired by Pełczyński's decomposition method in Banach spaces, we introduce the notion of Schroeder-Bernstein quadruples for Banach spaces. Then we use some Banach spaces constructed by W. T. Gowers and B. Maurey in 1997 to characterize them.
∗ Supported by Research grants GAUK 190/96 and GAUK 1/1998We prove that the dual unit ball of the space C0 [0, ω1 ) endowed
with the weak* topology is not a Valdivia compact. This answers a question
posed to the author by V. Zizler and has several consequences. Namely, it
yields an example of an affine continuous image of a convex Valdivia compact
(in the weak* topology of a dual Banach space) which is not Valdivia,
and shows that the property of the dual unit ball being Valdivia is not an
isomorphic...
Let , . We construct a function which has Lipschitz Fréchet derivative on but is not a d.c. function.
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