## 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 language | English (US) |
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Pages (from-to) | 193-198 |

Number of pages | 6 |

Journal | Proceedings of the American Mathematical Society |

Volume | 121 |

Issue number | 1 |

DOIs | |

State | Published - 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