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Arveson nests and operator factorization along commutative subspace lattices


Authors: John Daughtry and Ronald Johns
Journal: Proc. Amer. Math. Soc. 107 (1989), 943-947
MSC: Primary 47A68; Secondary 47A15, 47D99
DOI: https://doi.org/10.1090/S0002-9939-1989-0975636-5
MathSciNet review: 975636
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Abstract: Similar commutative subspace lattices (CSL's) are shown to be unitarily equivalent if certain sublattices (which may be taken to be nests!) are unitarily equivalent and a technical condition is satisfied. This result provides a connection between existing results for arbitrary similarities of countable CSL's and similarities of general CSL's by operators near the identity. One consequence is the generalizaton to CSL's of a theorem of David Pitts on the relationship between similarity and unitary equivalence of nests he calls "injective."


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DOI: https://doi.org/10.1090/S0002-9939-1989-0975636-5
Keywords: Commutative subspace lattice algebra, operator factorization, nest, conditional expectations on von Neumann algebras
Article copyright: © Copyright 1989 American Mathematical Society

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