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Compact Groups of Operators on Subproportional Quotients of $l^m_1$

  Published:2000-10-01
 Printed: Oct 2000
  • Piotr Mankiewicz
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Abstract

It is proved that a ``typical'' $n$-dimensional quotient $X_n$ of $l^m_1$ with $n = m^{\sigma}$, $0 < \sigma < 1$, has the property $$ \Average \int_G \|Tx\|_{X_n} \,dh_G(T) \geq \frac{c}{\sqrt{n\log^3 n}} \biggl( n - \int_G |\tr T| \,dh_G (T) \biggr), $$ 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.
MSC Classifications: 46B20, 46B09 show english descriptions Geometry and structure of normed linear spaces
Probabilistic methods in Banach space theory [See also 60Bxx]
46B20 - Geometry and structure of normed linear spaces
46B09 - Probabilistic methods in Banach space theory [See also 60Bxx]
 

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