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

Evgeny M. Semenov; Boris S. Tsirelson

doi:10.4171/zaa/73

JournalszaaVol. 2, No. 4pp. 367–373

The problem of smallness of operator blocks in $L_{p}$ spaces (in Russian)

Evgeny M. Semenov
Voronezh State University, Russian Federation
Boris S. Tsirelson
Tel Aviv University, Israel

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Abstract

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 $∥ Q_{e} A Q_{f} ∥_{L_{p} \to L_{p}} \geq 1$ 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 $e$ .

Cite this article

Evgeny M. Semenov, Boris S. Tsirelson, The problem of smallness of operator blocks in $L_{p}$ spaces (in Russian) . Z. Anal. Anwend. 2 (1983), no. 4, pp. 367–373

DOI 10.4171/ZAA/73