Cycles and 1-unconditional matrices

Details Cycles and 1-unconditional matrices Cycles and 1-unconditional matrices

2001-02-19

arxiv.org/abs/math/0102146v2

Mathematics

Functional Analysis

29 pages. This new version computes explicitly certain unconditionality constants, shows how our results generalize Varopoulos

Scientific paper

We characterize the 1-unconditional subsequences of the canonical basis (e_rc) of elementary matrices in the Schatten-von-Neumann class S^p . The set I of couples (r,c) must be the set of edges of a bipartite graph without cycles of even length 4<=l<=p if p is an even integer, and without cycles at all if p is a positive real number that is not an even integer. In the latter case, I is even a Varopoulos set of V-interpolation of constant 1. We also study the metric unconditional approximation property for the space S^p_I spanned by (e_rc)_{(r,c)\in I} in S^p .

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