# 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

## 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 $\|Q_eAQ_f\|_{L_p \to L_p} \geq 1$ 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 $e$.

## 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