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Proceedings of the American Mathematical Society

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



Essentially triangular algebras

Authors: J. A. Erdos and A. Hopenwasser
Journal: Proc. Amer. Math. Soc. 96 (1986), 335-339
MSC: Primary 47D25
MathSciNet review: 818468
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Abstract: If $ \mathcal{N}$ is a nest, then the set of all bounded linear operators $ T$ such that $ TP - PTP$ is compact for all $ P$ in $ \mathcal{N}$ is the essentially triangular algebra associated with $ \mathcal{N}$. Put another way, essentially triangular algebras are the inverse images under the Calkin map of nest-subalgebras of the Calkin algebra. J. Deddens has characterized nest algebras in terms of operators whose half-orbits under similarity by a positive invertible operator are bounded in norm. This paper, by substituting essential norms for norms, provides a related characterization of essentially triangular algebras.

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Article copyright: © Copyright 1986 American Mathematical Society