Essentially triangular algebras

Erdos, J. A.; Hopenwasser, A.

doi:10.1090/S0002-9939-1986-0818468-8

Essentially triangular algebras
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by J. A. Erdos and A. Hopenwasser PDF

Proc. Amer. Math. Soc. 96 (1986), 335-339 Request permission

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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