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Compact Groups of Operators on Subproportional Quotients of l1m
Published online by Cambridge University Press: 20 November 2018
Abstract
It is proved that a “typical” $n$-dimensional quotient ${{X}_{n}}$ of $l_{1}^{m}$ with $n={{m}^{\sigma }},0<\sigma <1$, has the property
for every compact group $G$ of operators acting on ${{X}_{n}}$, where ${{d}_{G}}(T)$ stands for the normalized Haar measure on $G$ and the average is taken over all extreme points of the unit ball of ${{X}_{n}}$. Several consequences of this estimate are presented.
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- Copyright © Canadian Mathematical Society 2000
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