Fatou's Lemma in Reflexive Banach Spaces
β Scribed by S.I. Suslov
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 118 KB
- Volume
- 199
- Category
- Article
- ISSN
- 0022-247X
No coin nor oath required. For personal study only.
β¦ Synopsis
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.
π SIMILAR VOLUMES
We investigate whether the Q-reflexive Banach spaces have the following properties: containment of l p , reflexivity, Dunford-Pettis property, etc.
Here Z denotes the dual of Z, and β³# denotes the polar of β³ taken in Z.
In this note the following new version of the Schwarz lemma is proved: If f is a holomorphic function mapping a bounded convex domain D D of a complex Banach 1 Ε½ . space into a convex domain D D of another complex Banach space and f a s b, 2 then the image by f of the set of points in D D lying at a