Invariance of projections in the diagonal of a nest algebra

Author:
John Daughtry

Journal:
Proc. Amer. Math. Soc. **102** (1988), 117-120

MSC:
Primary 47C05,; Secondary 47D25

MathSciNet review:
915727

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Abstract: The study of operator factorization along commutative subspace lattices which are not nests leads to the investigation of the mapping which takes an orthogonal projection in the diagonal of a nest algebra to the projection on the closure of the range of *AQ* for certain bounded linear operators . The purpose of this paper is to demonstrate that if is an operator leaving the range of invariant, is an element of the "Larson radical" of is invertible, belongs to , and is in the diagonal of , then . For example, if is in the Jacobson radical of and is a nonzero scalar, it follows that if and only if belongs to the diagonal of . Examples of the applications to operator factorization and unitary equivalence of sets of projections are given.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1988-0915727-7

Keywords:
Nest algebra,
CSL algebra,
factorization of positive operators

Article copyright:
© Copyright 1988
American Mathematical Society