A characterization of nonunital operator algebras

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Abstract

We give an abstract matrix norm characterization for operator algebras with contractive approximate identities by using the second dual approach. We show that if A is an L-Banach pseudoalgebra with a contractive approximate identity, then the second dual A** of A is a unital L-Banach pseudoalgebra containing A as a subalgebra. It follows from the Blecher-Ruan- Sinclair characterization theorem for unital operator algebras that A** is completely isometrically unital isomorphic to a concrete unital operator algebra on a Hubert space. Thus A is completely isometrically isomorphic to a concrete nondegenerate operator algebra with a contractive approximate identity.

Original languageEnglish (US)
Pages (from-to)193-198
Number of pages6
JournalProceedings of the American Mathematical Society
Volume121
Issue number1
DOIs
StatePublished - May 1994

Keywords

  • Completely bounded maps
  • L-Banach pseudoalgberas
  • L-matricially normed spaces
  • Operator algebras
  • Operator duals

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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