Property l and asymptotic abelianness for w*-algebras

Document Type

Article

Publication Date

1-1-1980

Abstract

(i) Let A be a finite W*-algebra acting on a separable Hilbert space and having no abelian direct summand. If A is asymptotically abelian, then A, has property L. (ii) Let A be a finite W*-algebra acting on a separable Hilbert space. Then A ⊗ B(h), h a separable infinite dimensional Hilbert space, is not asymptotically abelian. (iii) Type II∞W*-algebras are not asymptotically abelian. (iv) Noncommutative type I W*-algebras are not asymptotically abelian. (v) The type III factor B=P⊗A(G) is not asymptotically abelian. B produces uncountably many nonisomorphic nonasymptotically abelian factors of type III and establishes an example of a purely infinite factor that has property L but is not asymptotically abelian. © 1980 American Mathematical Society.

Identifier

84966220778 (Scopus)

Publication Title

Proceedings of the American Mathematical Society

External Full Text Location

https://doi.org/10.1090/S0002-9939-1980-0574521-2

e-ISSN

10886826

ISSN

00029939

First Page

125

Last Page

129

Issue

1

Volume

80

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