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Duality and Twisted Sums of Banach Spaces

✍ Scribed by Félix Cabello Sánchez; Jesús M.F. Castillo

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
140 KB
Volume
175
Category
Article
ISSN
0022-1236

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✦ Synopsis

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, DusseldorfÂWuppertal, Jan Feb. 1987] and another posed by D@ az et al. in [Bull. Polish Acad. Sci. Math. 40 (1992), 221 224]). Precisely, we construct an exact sequence 0 Ä l 2 Ä D Ä W* Ä 0 in which W* is a separable dual and D is not isomorphic to a dual space. We also show the existence of an exact sequence 0 Ä Y Ä X Ä Z Ä 0 where both Y and Z are dual spaces and X is not even complemented in its bidual. To do that we perform a study of the basic questions on duality from the point of view of exact sequences of Banach spaces.

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