Properties of Q-Reflexive Banach Spaces
โ Scribed by M. Venkova
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 106 KB
- Volume
- 264
- Category
- Article
- ISSN
- 0022-247X
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โฆ Synopsis
We investigate whether the Q-reflexive Banach spaces have the following properties: containment of l p , reflexivity, Dunford-Pettis property, etc.
๐ SIMILAR VOLUMES
Here Z denotes the dual of Z, and โณ# denotes the polar of โณ taken in Z.
A version of an approximate Fatou Lemma for a uniformly integrable sequence of functions with values in a reflexive Banach space is proved. The usual assumption that this sequence is pointwisely dominated in norm by a real valued integrable function is omitted.
Let X be a Banach space with a basis. We prove the following characterizations: (i) X is finite-dimensional if and only if every power-bounded operator is uniformly ergodic. (ii) X is reflexive if and only if every power-bounded operator is mean ergodic. (iii) X is quasi-reflexive of order one if