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THE OPERATOR SHIFT SPACE

Published online by Cambridge University Press:  04 February 2008

Timur Oikhberg
Timur Oikhberg
Affiliation:
Department of Mathematics, University of California, Irvine, Irvine, CA 92697, USA ([email protected])
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Abstract

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We construct and examine an operator space $X$, isometric to $\ell_2$, such that every completely bounded map from its subspace $Y$ into $X$ is a compact perturbation of a linear combination of multiples of a shift of given multiplicity and their adjoints. Moreover, every completely bounded map on $X$ is a Hilbert–Schmidt perturbation of such a linear combination.

Keywords

Primary 46L0746L1047L25operator spacescompletely bounded mapscompletely indecomposable spacesshift operator
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 51 , Issue 1 , February 2008 , pp. 229 - 263
Copyright
Copyright © Edinburgh Mathematical Society 2008