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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Factorization in operator algebras

Author: Baruch Solel
Journal: Proc. Amer. Math. Soc. 102 (1988), 613-618
MSC: Primary 46L10; Secondary 47A68, 47D25
MathSciNet review: 928990
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Abstract: Let $ M \subseteq B(H)$ be a $ \sigma $-finite von Neumann algebra and let $ \mathcal{L}$ be a lattice of projections associated with a unitary representation $ \left\{ {{W_t}} \right\}$ of a compact group with an ordered dual. ( $ \mathcal{L}$ is not necessarily contained in $ M$.) Assume that $ M$ is invariant under ad $ {W_t}$ for every $ t$.

Then, whenever $ T$ is an invertible operator in $ M$ that can be factored as $ T = UA$ where $ U$ is a unitary operator in $ B(H)$ and $ A$ lies in $ \operatorname{alg} \mathcal{L} \cap {(\operatorname{alg} \mathcal{L}{\text{)}}^{ - 1}}$, then $ U$ and $ A$ can be chosen in $ M$.

As corollaries we derive results about factorization with respect to CSL subalgebras and analytic subalgebras of von Neumann algebras.

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Keywords: Invertible operator, factorization, analytic subalgebra, CSL subalgebra, von Neumann algebra
Article copyright: © Copyright 1988 American Mathematical Society

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