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Cycles and 1-unconditional matrices
Abstract
International audienceWe characterise 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- info:eu-repo/semantics/article
- Journal articles
- Schatten-von-Neumann class
- Schur product
- graph with a given girth
- 1-unconditional basic sequence
- metric unconditional approximation property
- V-Sidon set
- lacunary set
- 47B10, 46B15, 46B04, 43A46, 05C38, 46B28
- [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA]
- [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]