This is an announcement for the paper "Frames and operators in Schatten classes" by Hu Bingyang, Le Hai Khoi, and Kehe Zhu.

Abstract: Let $T$ be a compact operator on a separable Hilbert space $H$. We show that, for $2\le p<\infty$, $T$ belongs to the Schatten class $S_p$ if and only if ${|Tf_n|}\in \ell^p$ for \emph{every} frame ${f_n}$ in $H$; and for $0<p\le2$, $T$ belongs to $S_p$ if and only if ${|Tf_n|}\in\ell^p$ for \emph{some} frame ${f_n}$ in $H$. Similar conditions are also obtained in terms of the sequence ${\langle Tf_n,f_n\rangle}$ and the double-indexed sequence ${\langle Tf_n,f_m\rangle}$.

Archive classification: math.FA

Mathematics Subject Classification: 47B10, 46A35, 46B15

Remarks: 27 pages

Submitted from: kzhu@math.albany.edu

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1302.2490

or

http://arXiv.org/abs/1302.2490