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

MathSciNet review:
975636

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Abstract | References | Similar Articles | Additional Information

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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Additional Information

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