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Proceedings of the American Mathematical Society

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

 
 

 

Operator ranges and completely bounded homomorphisms


Author: D. Benjamin Mathes
Journal: Proc. Amer. Math. Soc. 107 (1989), 155-164
MSC: Primary 47D25; Secondary 47A15, 47C05
DOI: https://doi.org/10.1090/S0002-9939-1989-0979229-5
MathSciNet review: 979229
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Abstract: In this paper it is shown that the set of invariant operator ranges that induce completely bounded homomorphisms is a sublattice of $ \operatorname{Lat}_{1/2}\mathfrak{A}$, when $ \mathfrak{A}$ is any norm closed algebra of operators on a Hilbert space. A characterization of this sublattice is given, and several concrete examples are discussed.


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DOI: https://doi.org/10.1090/S0002-9939-1989-0979229-5
Keywords: Invariant operator range, completely bounded homomorphism
Article copyright: © Copyright 1989 American Mathematical Society

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