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A superreflexive Banach space with a finite dimensional decomposition so that no large subspace has a basis. (English) Zbl 0721.46007

Summary: The main result of the present paper is the construction of a Banach space with finite dimensional decomposition in which no large subspace has a basis. This answers a question raised by P. Casazza. The paper also contains various results on subspaces of direct sums of spaces and an investigation of spaces closely related to spaces constructed by the first named author.

MSC:

46B15 Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces
46B10 Duality and reflexivity in normed linear and Banach spaces
46B28 Spaces of operators; tensor products; approximation properties
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