$\mathcal {C}_{p}$-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.References
- William Arveson, Interpolation problems in nest algebras, J. Functional Analysis 20 (1975), no. 3, 208–233. MR 0383098, DOI 10.1016/0022-1236(75)90041-5
- J. A. Erdos, Triangular integration on symmetrically normed ideals, Indiana Univ. Math. J. 27 (1978), no. 3, 401–408. MR 473892, DOI 10.1512/iumj.1978.27.27029
- Thomas Fall, William Arveson, and Paul Muhly, Perturbations of nest algebras, J. Operator Theory 1 (1979), no. 1, 137–150. MR 526295
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