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

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).