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Cycles and 1-unconditional matrices
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 .Comment: 29 pages. This new version computes explicitly certain
unconditionality constants, shows how our results generalize Varopoulos' work
on V-Sidon sets, investigates the metric unconditional approximation property
in the same contex
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