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Proceedings of the American Mathematical Society

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

 

 

$ \mathcal{C}\sb{p}$-perturbations of nest algebras


Author: Gareth J. Knowles
Journal: Proc. Amer. Math. Soc. 92 (1984), 37-40
MSC: Primary 47A45; Secondary 47A15, 47D25
DOI: https://doi.org/10.1090/S0002-9939-1984-0749885-0
MathSciNet review: 749885
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Abstract: Given the ideal $ {{\mathcal C}_p}$ and a nest algebra $ {\mathcal A}$ in $ {\mathcal L}(H)$ there are two corresponding subalgebras of $ {\mathcal L}(H)$. The first consists of all $ {{\mathcal C}_p}$-perturbations of $ {\mathcal A}$. The second, a natural generalization of the quasitriangular algebra corresponding to $ {\mathcal A}$, consists of all $ T$ in $ {\mathcal L}(H)$ with $ E \to (I - E)TE$ continuous from Lat $ {\mathcal A}$ into $ {{\mathcal C}_p}$. Necessary and sufficient conditions are given for these algebras to be identical.


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DOI: https://doi.org/10.1090/S0002-9939-1984-0749885-0
Article copyright: © Copyright 1984 American Mathematical Society