Journal of Operator Theory

Volume 34, Issue 1, Summer 1995 pp. 17-56.

Continuity of Schur block-multiplication maps with respect to various topologies

Authors: Leo Livshits
Author institution:Department of Mathematics and CS, Colby College, Waterville, ME 04901, USA

Summary: We consider maps induced on the space of bounded operator matrices via left Schur multiplication by a fixed Schur multiplier matrix. The main goal is to give a complete characterization of those multipliers that induce continuous maps when initial and final topologies are chosen from among the weak, the strong and the norm topologies.

Keywords: Schur (Hadamard) block-multiplication, Schur multipliers, Block- matrices.

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