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Proceedings of the London Mathematical Society 2006 93(3):761-790; doi:10.1017/S0024611506015899
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© London Mathematical Society

Cycles and 1-Unconditional Matrices

Stefan Neuwirth

Laboratoire de Mathématiques, Université de Franche-Comté 25030 Besançon cedex, France neuwirth{at}math.univ-fcomte.fr

Received 12 October 2004. Revision received 4 November 2005.

We characterise the 1-unconditional subsets (erc(r,c) isin I of the set of elementary matrices in the Schatten–von-Neumann class Sp. 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 space Formula spanned by (erc)(r,c) isin I in Sp. 2000 Mathematics Subject Classification 47B10, 46B15, 46B04, 43A46, 05C38, 46B28.


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