The Long Homology Sequence for Quasi-Banach Spaces, with Applications

The Long Homology Sequence for Quasi-Banach Spaces, with Applications We establish the existence of long homology sequences in the category of quasi-Banach spaces, with values in a certain category of topological vector spaces. We derive from that new results about the structure of twisted sums of quasi-Banach and Banach spaces. Sample result: let A and B be subspaces of Lp, with 0 < p < 1. If Lp/A and Lp/B are isomorphic then so are A* and B*. In particular, if A and B are finite dimensional, then Lp/A and Lp/B are isomorphic if and only if dim(A) = dim(B). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

The Long Homology Sequence for Quasi-Banach Spaces, with Applications

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Publisher
Kluwer Academic Publishers
Copyright
Copyright © 2004 by Kluwer Academic Publishers
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-002-2465-y
Publisher site
See Article on Publisher Site

Abstract

We establish the existence of long homology sequences in the category of quasi-Banach spaces, with values in a certain category of topological vector spaces. We derive from that new results about the structure of twisted sums of quasi-Banach and Banach spaces. Sample result: let A and B be subspaces of Lp, with 0 < p < 1. If Lp/A and Lp/B are isomorphic then so are A* and B*. In particular, if A and B are finite dimensional, then Lp/A and Lp/B are isomorphic if and only if dim(A) = dim(B).

Journal

PositivitySpringer Journals

Published: Jul 25, 2002

References

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