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Compact groups of operators on proportional quotients ofl n1

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Abstract

It is proved that for arbitrarymεℕ and for a sufficiently nontrivial compact groupG of operators acting on a “typical”n-dimensional quotientX n ofl m1 withm=(1+δ)n, there is a constantc=c(δ) such that\(\mathop {sup}\limits_{\left\| x \right\| = 1} \smallint _G \left\| {Tx} \right\|dh_G (T) \geqslant c\sqrt n /logn\)

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Authors and Affiliations

  1. Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950, Warsaw, Poland

    Piotr Mankiewicz

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  1. Piotr Mankiewicz
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Correspondence to Piotr Mankiewicz.

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Supported in part by KBN grant no. 2 P03A 034 10.

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Mankiewicz, P. Compact groups of operators on proportional quotients ofl n1 . Isr. J. Math. 109, 75–91 (1999). https://doi.org/10.1007/BF02775028

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  • DOI: https://doi.org/10.1007/BF02775028

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