Normalizers of nest algebras

Coates, Keith

doi:10.1090/S0002-9939-98-04222-1

Normalizers of nest algebras
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by Keith J. Coates

Proc. Amer. Math. Soc. 126 (1998), 159-165

DOI: https://doi.org/10.1090/S0002-9939-98-04222-1

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Erratum: Proc. Amer. Math. Soc. 126 (1998), 2511-2512.

Abstract:

For a nest $\mathcal {N}$ with associated nest algebra $\mathcal {A}_{\mathcal {N}}$, we define $\mathcal {S}_{\mathcal {N}}$, the normalizer of $\mathcal {A}_{\mathcal {N}}$. We develop a characterization of elements of $\mathcal {S}_{\mathcal {N}}$ based on certain order homomorphisms of $\mathcal {N}$ into itself. This characterization enables us to prove several structure theorems.

References

Kenneth R. Davidson, Nest algebras, Pitman Research Notes in Mathematics Series, vol. 191, Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1988. Triangular forms for operator algebras on Hilbert space. MR 972978
J. A. Erdos and S. C. Power, Weakly closed ideals of nest algebras, J. Operator Theory 7 (1982), no. 2, 219–235. MR 658610
Richard V. Kadison and John R. Ringrose, Fundamentals of the theory of operator algebras. Vol. I, Pure and Applied Mathematics, vol. 100, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York, 1983. Elementary theory. MR 719020
Stephen C. Power, Limit algebras: an introduction to subalgebras of $C^*$-algebras, Pitman Research Notes in Mathematics Series, vol. 278, Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1992. MR 1204657
J. R. Ringrose, On some algebras of operators, Proc. London Math. Soc. (3) 15 (1965), 61–83. MR 171174, DOI 10.1112/plms/s3-15.1.61