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arXiv · 1808.06938

The Hoffman-Rossi theorem for operator algebras

David P. Blecher·Luis C. Flores·Beate G. Zimmer
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Abstract

We study possible noncommutative (operator algebra) variants of the classical Hoffman-Rossi theorem from the theory of function algebras. In particular we give a condition on the range of a contractive weak* continuous homomorphism defined on an operator algebra A, which is necessary and sufficient (in the setting we explain) for a positive weak* continuous extension to any von Neumann algebra containing A.

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David P. Blecher, Luis C. Flores, Beate G. Zimmer. 2018-08-21. The Hoffman-Rossi theorem for operator algebras. https://arxiv.org/abs/1808.06938

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