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 | References | Similar Articles | Additional Information

Abstract: Let be a -finite von Neumann algebra and let be a lattice of projections associated with a unitary representation of a compact group with an ordered dual. ( is not necessarily contained in .) Assume that is invariant under ad for every .

Then, whenever is an invertible operator in that can be factored as where is a unitary operator in and lies in , then and can be chosen in .

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

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1988-0928990-3

Keywords:
Invertible operator,
factorization,
analytic subalgebra,
CSL subalgebra,
von Neumann algebra

Article copyright:
© Copyright 1988
American Mathematical Society