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Cycles and 1-unconditional matrices
, 2008
"... We characterize the 1-unconditional subsets (erc)(r,c)∈I of the set of elementary matrices in the Schatten-von-Neumann class S p. The set of couples I 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 po ..."
Abstract
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We characterize the 1-unconditional subsets (erc)(r,c)∈I of the set of elementary matrices in the Schatten-von-Neumann class S p. The set of couples I 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 (erc)(r,c)∈I in S p. 1
