Some applications of direct integral decompositions of W*-algebras

Document Type

Article

Publication Date

1-1-1983

Abstract

Let Ҩ be a W*-algebra and let A ∈ Ҩ. ��(Ҩ) and C(A) represent certain convex subsets of Ҩ. We prove the following via direct integral theory: If Ҩ is of type I∞, II∞, then C(A) - {0} iff A ∈ ��(Ҩ). If Ҩ is of type I or II, then ��(Ҩ) is strongly dense in Ҩ. If Ҩ is of type I∞, II∞, or III and �� is a W*-subalgebra of Ҩ, we give sufficient conditions for a Schwartz map P of Ҩ into �� to annihilate ��(Ҩ). Several preliminary lemmas that are useful for direct integral theory are also proved. © 1983 American Mathematical Society.

Identifier

84967780437 (Scopus)

Publication Title

Transactions of the American Mathematical Society

External Full Text Location

https://doi.org/10.1090/S0002-9947-1983-0709576-2

ISSN

00029947

First Page

677

Last Page

689

Issue

2

Volume

279

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