Cycles and 1-uncondictional matrices

• Autores: Stefan Neuwirth
• Localización: Proceedings of the London Mathematical Society, ISSN 0024-6115, Vol. 93, Nº 3, 2006, págs. 761-790
• Idioma: inglés
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• Resumen

  • We characterise the 1-unconditional subsets $(\mathrm{e}_{rc})_{(r,c) \in I}$ of the set of elementary matrices in the Schatten¿von-Neumann class $\mathrm{S}^p$. The set of couples $I$ must be the set of edges of a bipartite graph without cycles of even length $4 \lel \le p$ 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 $\mathrm{S}^p_I$ spanned by $(\mathrm{e}_{rc})_{(r,c) \in I}$ in $\mathrm{S}^p$.