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Journal of Operator Theory

Volume 46, Issue 2, Fall 2001  pp. 281-288.

Adjoining a unit to an operator algebra

Authors Ralf Meyer
Author institution: SFB Geometrische Strukturen in der Mathematik, Universitaet Munster, Hittorfstrasse 27, 48149 Munster, Germany

Summary:  We show that the matricial norms of a non-unital operator algebra determine those of the algebra obtained by adjoining a unit to it. As applications, we classify two-dimensional unital operator algebras and show that the algebra of bounded holomorphic functions on a strongly pseudoconvex domain has a contractive representation that is not completely contractive.

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