Some abelian Banach algebras of operators on the matricial factor

Author:
A. Guyan Robertson

Journal:
Proc. Amer. Math. Soc. **109** (1990), 1063-1068

MSC:
Primary 46L10; Secondary 22D25, 43A30

MathSciNet review:
1009999

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Abstract: We show that, if is an amenable discrete group, then the set of completely bounded [completely positive] multiplication operators on is maximal abelian and norm- complemented in various sets of bounded [positive] operators on . Since there are many different amenable discrete groups which generate the matricial factor , this shows the set of completely bounded normal operators on contains uncountably many non-isomorphic maximal abelian subalgebras each of which is complemented by a positivity-preserving projection of norm one. Our results are closely related to [16], which considers the case of group -algebras of general locally compact groups.

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DOI:
https://doi.org/10.1090/S0002-9939-1990-1009999-X

Article copyright:
© Copyright 1990
American Mathematical Society