Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4591523 | Journal of Functional Analysis | 2011 | 30 Pages |
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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