Journal of Operator Theory

Volume 51, Issue 2, Spring 2004 pp. 435-453.

A double commutant theorem for operator algebras

Authors: David P. Blecher (1) and Baruch Solel (2)
Author institution: (1) Department of Mathematics, University of Houston, Houston, TX 77204-3008, USA
(2) Department of Mathematics, Technion, 32000 Haifa, Israel

Summary: Every unital nonselfadjoint operator algebra possesses canonical and functorial classes of faithful (even completely isometric) Hilbert space representations satisfying a double commutant theorem generalizing von Neumann's classical result. Examples and complementary results are given.

Keywords: Operator algebra, representation, double commutant, Hilbert\break module, dual algebra, generator

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