We give a negative answer to the three-space problem for the Banach space properties to be complemented in a dual space and to be isomorphic to a dual space (solving a problem of Vogt [Lectures held in the Functional Analysis Seminar, DusseldorfΓWuppertal, Jan Feb. 1987] and another posed by D@ az e
Countable Direct Sums of Banach Spaces
β Scribed by M. Valdivia
- Publisher
- John Wiley and Sons
- Year
- 1989
- Tongue
- English
- Weight
- 287 KB
- Volume
- 141
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
β¦ Synopsis
Let (XJF-1 be a sequence of infinite-dimensional BANACH spaces. We prove that 00 @ X, has a non-locally complete quotient if XI is not quasi-reflexive.
π SIMILAR VOLUMES
## Abstract We study the role that the axiom of choice plays in Tychonoff's product theorem restricted to countable families of compact, as well as, LindelΓΆf metric spaces, and in disjoint topological unions of countably many such spaces. (Β© 2004 WILEYβVCH Verlag GmbH & Co. KGaA, Weinheim)
A HAUSDORFF locally convex space is said to be c,-barrelled (respectively cu-barrelled) if each sequence in the dual space t h a t converges weakly to 0 (res!,r:ctively t h a t is weakly ?.~oundecl), is equicontinuous. It is proved that if a c,,-barrelled space E has dual E' weakly sequentially comp