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Schur multiplier projections on the von Neumann-Schatten classes

J. Operator Theory, 53 (2005), 251-272

Ian Doust and T.A. Gillespie

Address: School of Mathematics, University of New South Wales, Sydney NSW 2052, Australia

Email:  i.doust@unsw.edu.au

Abstract: For $1 \le p < \infty$ let $C_p$ denote the usual von Neumann-Schatten ideal of compact operators on $\ell^2$. The standard basis of $C_p$ is a conditional one and so it is of interest to be able to identify the sets of coordinates for which the corresponding projection is bounded. In this paper we survey and extend the known classes of bounded projections of this type. In particular we show that some recent results from spectral theory allow one to prove boundedness of a projection by checking simple geometric conditions on the associated set of coordinates.

Key words and phrases. Von Neumann-Schatten classes, Schur multipliers

2000 Mathematics Subject Classification. Primary 47B49, 47B10. Secondary 46B15.

This paper appeared in the Journal of Operator Theory, The final version may differ from the preprint available below.
The preprint (dated 23/04/2003) is available in several forms: Please contact Ian if you have any trouble downloading the files.