Journal of Operator Theory

Volume 53, Issue 2, Spring 2005 pp. 251-272.

Schur multiplier projections on the von Neumann-Schatten classes

Authors: Ian Doust (1) and T.A. Gillespie (2)
Author institution: (1) School of Mathematics, University of New South Wales, Sydney, NSW 2052, Australia
(2) Department of Mathematics and Statistics, University of Edinburgh, James Clerk Maxwell Building, The King's Buildings, Edinburgh EH9~3JZ, Scotland

Summary: For $1 \leqslant p < \infty$ 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.

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