Arveson nests and operator factorization along commutative subspace lattices

Daughtry, John; Johns, Ronald

doi:10.1090/S0002-9939-1989-0975636-5

Arveson nests and operator factorization along commutative subspace lattices
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by John Daughtry and Ronald Johns PDF

Proc. Amer. Math. Soc. 107 (1989), 943-947 Request permission

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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Modular theory in operator algebras