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EMBEDDING $\ell_{\infty}$ INTO THE SPACE OF BOUNDED OPERATORS ON CERTAIN BANACH SPACES

Published online by Cambridge University Press:  19 December 2006

G. ANDROULAKIS ,
K. BEANLAND ,
S. J. DILWORTH  and
F. SANACORY
G. ANDROULAKIS
Affiliation:
Department of Mathematics, University of South Carolina, Columbia, SC 29208, USAgiorgis@math.sc.edu, beanland@math.sc.edu, dilworth@math.sc.edu, sanacory@math.sc.edu
K. BEANLAND
Affiliation:
Department of Mathematics, University of South Carolina, Columbia, SC 29208, USAgiorgis@math.sc.edu, beanland@math.sc.edu, dilworth@math.sc.edu, sanacory@math.sc.edu
S. J. DILWORTH
Affiliation:
Department of Mathematics, University of South Carolina, Columbia, SC 29208, USAgiorgis@math.sc.edu, beanland@math.sc.edu, dilworth@math.sc.edu, sanacory@math.sc.edu
F. SANACORY
Affiliation:
Department of Mathematics, University of South Carolina, Columbia, SC 29208, USAgiorgis@math.sc.edu, beanland@math.sc.edu, dilworth@math.sc.edu, sanacory@math.sc.edu
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Abstract

Sufficient conditions are given on a Banach space $X$ which ensure that $\ell_{\infty}$ embeds in ${\mathcal L}\, (X)$, the space of all bounded linear operators on $X$. A basic sequence $(e_n)$ is said to be quasisubsymmetric if for any two increasing sequences $(k_n)$ and $(\ell_n)$ of positive integers with $k_n \leq \ell_n$ for all $n$, $(e_{k_n})$ dominates $(e_{\ell_n})$. If a Banach space $X$ has a seminormalized quasisubsymmetric basis then $\ell_{\infty}$ embeds in ${\mathcal L}\, (X)$.

Keywords

46B28 (primary)46B03 (secondary)
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 38 , Issue 6 , December 2006 , pp. 979 - 990
Copyright
The London Mathematical Society 2006

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