On Quasi-Chebyshev Subspaces of Banach Spaces
β Scribed by H. Mohebi
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 125 KB
- Volume
- 107
- Category
- Article
- ISSN
- 0021-9045
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π SIMILAR VOLUMES
Let (X, β’ ) be a Banach space. We study asymptotically bounded quasi constricted representations of an abelian semigroup IP in L(X), i. e. representations (Tt) tβIP which satisfy the following conditions: i) lim tββ Ttx < β for all x β X. ii) X 0 := {x β X : lim tββ Ttx = 0} is closed and has finite
W. Schachermayer showed that even 1-complemented subspaces of Banach spaces with property β£ can fail this property. However, we prove in this paper that spaces with property β£ satisfy an hereditary property. We obtain, as a conse-Ε½ . quence, that spaces with properties β£ and H cannot be reflexive an
We show that any series Γ K of operators in L X, Y that is unconditionally n n convergent in the weak operator topology and satisfies the condition that Γ K n g F n is a compact operator for every index set F : β«ήβ¬ is unconditionally convergent in the uniform operator topology if and only if X \*, t
## Abstract This article deals with the relationship between an operator ideal and its natural polynomial extensions. We define the concept of coherent sequence of polynomial ideals and also the notion of compatibility between polynomial and operator ideals. We study the stability of these properti