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Cycles and 1‐Unconditional Matrices
Author(s) -
Neuwirth Stefan
Publication year - 2006
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1017/s0024611506015899
Subject(s) - mathematics , combinatorics , bipartite graph , integer (computer science) , graph , class (philosophy) , space (punctuation) , set (abstract data type) , discrete mathematics , constant (computer programming) , computer science , linguistics , philosophy , artificial intelligence , programming language
We characterise the 1‐unconditional subsets (e rc ( 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 ⩽ 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 spaceS I p spanned by (e rc )( r,c ) ∈ I in S p . 2000 Mathematics Subject Classification 47B10, 46B15, 46B04, 43A46, 05C38, 46B28.