On the complexity of some inevitable classes of separable Banach spaces.
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In this paper, we study the descriptive complexity of some inevitable classes of Banach spaces. Precisely, as shown in [Go], every Banach space either contains a hereditarily indecomposable subspace or an unconditional basis, and, as shown in [FR], every Banach space either contains a minimal subspace or a continuously tight subspace. In these notes, we study the complexity of those inevitable classes as well as the complexity of containing a subspace in any of those classes.
SubjectMinimal Banach spaces,
continuously tight Banach spaces
descriptive set theory
Banach spaces dichotomies
Date available in INDIGO2018-02-13T10:30:06Z
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SHAW, SEN-YEN. (1977)