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Zeitschrift für Analysis und ihre Anwendungen


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Volume 2, Issue 4, 1983, pp. 367–373
DOI: 10.4171/ZAA/73

Published online: 1983-08-31

The problem of smallness of operator blocks in $L_p$ spaces (in Russian)

Evgeny M. Semenov[1] and Boris S. Tsirelson[2]

(1) Voronezh State University, Russian Federation
(2) Tel Aviv University, Israel

For a given $p \in (1,\infty)$ the paper deals with the construction of an operator $A$, which is bounded in $L_p$, and for which $\|Q_eAQ_f\|_{L_p \to L_p} \geq 1$ holds for any sets $e,f \subset [0, 1]$ with positive measure. Here, $Q_e$ denotes the multiplication operator with the characteristic function of the set $e$.

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Semenov Evgeny, Tsirelson Boris: The problem of smallness of operator blocks in $L_p$ spaces (in Russian) . Z. Anal. Anwend. 2 (1983), 367-373. doi: 10.4171/ZAA/73