JournalszaaVol. 2, No. 4pp. 367–373

The problem of smallness of operator blocks in LpL_p spaces (in Russian)

  • Evgeny M. Semenov

    Voronezh State University, Russian Federation
  • Boris S. Tsirelson

    Tel Aviv University, Israel
The problem of smallness of operator blocks in $L_p$ spaces (in Russian)  cover
Download PDF

Abstract

For a given p(1,)p \in (1,\infty) the paper deals with the construction of an operator AA, which is bounded in LpL_p, and for which QeAQfLpLp1\|Q_eAQ_f\|_{L_p \to L_p} \geq 1 holds for any sets e,f[0,1]e,f \subset [0, 1] with positive measure. Here, QeQ_e denotes the multiplication operator with the characteristic function of the set ee.

Cite this article

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

DOI 10.4171/ZAA/73