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arXiv · 1011.3797

Operator algebras with contractive approximate identities

David P. Blecher·Charles John Read
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Abstract

We give several applications of a recent theorem of the second author, which solved a conjecture of the first author with Hay and Neal, concerning contractive approximate identities; and another of Hay from the theory of noncommutative peak sets, thereby putting the latter theory on a much firmer foundation. From this theorem it emerges there is a surprising amount of positivity present in any operator algebras with contractive approximate identity. We exploit this to generalize several results previously available only for $C^*$-algebras, and we give many other applications.

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David P. Blecher, Charles John Read. 2010-11-16. Operator algebras with contractive approximate identities. https://arxiv.org/abs/1011.3797

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