Vol. 212, No. 1, 2003

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Injective envelopes of C-algebras as operator modules

Michael Frank and Vern I. Paulsen

Vol. 212 (2003), No. 1, 57–69
Abstract

In this paper we give some characterizations of M. Hamana’s injective envelope I(A) of a C-algebra A in the setting of operator spaces and completely bounded maps. These characterizations lead to simplifications and generalizations of some known results concerning completely bounded projections onto C-algebras. We prove that I(A) is rigid for completely bounded A-module maps. This rigidity yields a natural representation of many kinds of multipliers as multiplications by elements of I(A). In particular, we prove that the(n times iterated) local multiplier algebra of A embeds into I(A).

Milestones
Received: 26 April 2000
Revised: 26 June 2001
Published: 1 November 2003
Authors
Michael Frank
Universität Leipzig
Mathematisches Institut
D-04109 Leipzig
Germany
Vern I. Paulsen
Dept. of Mathematics
University of Houston
TX 77204-3476