This is an announcement for the paper "Skipped blocking and other decompositions in Banach spaces" by Steven F. Bellenot.

Abstract: Necessary and sufficient conditions are given for when a sequence of finite dimensional subspaces (X_n) can be blocked to be a skipped blocking decompositon (SBD). The condition is order independent, so permutations of conditional basis, for example can be so blocked. This condition is implied if (X_n) is shrinking, or (X_n) is a permutation of a FDD, or if X is reflexive and (X_n) is separating. A separable space X has PCP, if and only if, every norming decomposition (X_n) can be blocked to be a boundedly complete SBD. Every boundedly complete SBD is a JT-decomposition.

Archive classification: Functional Analysis

Mathematics Subject Classification: 46B20 (Primary); 46B15, 46B22 (Secondary)

Report Number: FSU04-11

Remarks: 11 pages, 0 figures

The source file(s), skipB.tex: 42550 bytes, is(are) stored in gzipped form as 0408004.gz with size 13kb. The corresponding postcript file has gzipped size 65kb.

Submitted from: bellenot@math.fsu.edu

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