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Constructing unconditional finite dimensional decompositions. (English) Zbl 0745.46017

A fundamental problem in Banach space theory is to determine which properties of a Banach space are inherited by its complemented subspaces. Reflexivity, for example, is such a property. On the other hand, S. Szarek [Acta Math. 159, 81-98 (1987; Zbl 0637.46013)], has shown that there exists a complemented subspace of a Banach space with a basis which fails to have a basis. In this paper, the authors show that complemented subspaces of a Banach space with unconditional finite dimensional decompositions satisfying certain extra assumptions also have unconditional finite dimensional decompositions.
Reviewer: R.Young (Oberlin)

MSC:

46B15 Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces
46B20 Geometry and structure of normed linear spaces

Citations:

Zbl 0637.46013
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References:

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