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.