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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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$\mathcal {C}_{p}$-perturbations of nest algebras
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by Gareth J. Knowles PDF
Proc. Amer. Math. Soc. 92 (1984), 37-40 Request permission

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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Additional Information
  • © Copyright 1984 American Mathematical Society
  • 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