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arXiv · 1302.2490

Frames and operators in Schatten classes

Hu Bingyang·Le Hai Khoi·Kehe Zhu
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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 $0 \}$ and the double-indexed sequence $\{ \}$.

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Hu Bingyang, Le Hai Khoi, Kehe Zhu. 2013-02-11. Frames and operators in Schatten classes. https://arxiv.org/abs/1302.2490

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