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Normalizers of nest algebras

Author(s): Keith J. Coates
Journal: Proc. Amer. Math. Soc. 126 (1998), 159-165.
MSC (1991): Primary 47D25; Secondary 47D03
Errata: Proc. Amer. Math. Soc. 126 (1998), no. 8, 2511 - 2512.
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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:

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[KR]: R.V. Kadison and J.R. Ringrose, Fundamentals of the theory of operator algebras, Academic Press, Inc. New York, 1983. MR 85j:46099
[P]: S.C. Power, Limit algebras: an introduction to subalgebras of C $^{*}$ algebras, Pitman Research Notes, vol. 278, Longman Scientific and Technical, London, 1992. MR 94g:46001
[R]: J.R. Ringrose, On some algebras of operators, Proc. London Math. Soc. 15 (1965) 61-83. MR 30:1405


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