ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. 61,   2   (1992)
pp.   185-188

A NOTE ON CONTINUOUS RESTRICTIONS OF LINEAR MAPS BETWEEN BANACH SPACES
M. I. OSTROVSKII

Abstract.  This note is devoted to the answers to the following questions asked by V. I. Bogachev, B. Kirchheim and W. Schachermayer:\newline 1. Let $T\: l_1\to X$ be a linear map into the infinite dimensional Banach space $X$. Can one find a closed infinite dimensional subspace $Z\subset l_1$ such that $T\big|_\ZZ$ is continuous?\newline 2. Let $X=c_0$ or $X=l_p$ ($1<p<\infty$) and let $T\: X\to X$ be a linear map. Can one find a dense subspace $Z$ of $X$ such that \tz is continuous?

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