*Ian
Doust's *i*nformation pages*

## 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.