Invariance of projections in the diagonal of a nest algebra
Author:
John Daughtry
Journal:
Proc. Amer. Math. Soc. 102 (1988), 117120
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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 A. Hopenwasser, Hypercausal linear operators, SIAM J. Control and Optim. 6 (1984), 911919. MR 762629 (86c:47063)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939198809157277
PII:
S 00029939(1988)09157277
Keywords:
Nest algebra,
CSL algebra,
factorization of positive operators
Article copyright:
© Copyright 1988
American Mathematical Society
