[Banach] Abstract of a paper by Hu Bingyang, Le Hai Khoi, and Kehe Zhu

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