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Abstract: We give several applications of a recent theorem of the second author, whichsolved a conjecture of the first author with Hay and Neal, concerningcontractive approximate identities; and another of Hay from the theory ofnoncommutative peak sets, thereby putting the latter theory on a much firmerfoundation. From this theorem it emerges there is a surprising amount ofpositivity present in any operator algebras with contractive approximateidentity. We exploit this to generalize several results previously availableonly for $C^*$-algebras, and we give many other applications.



Author: David P. Blecher, Charles John Read

Source: https://arxiv.org/







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