| Autor: |
Rajarama BHAT, B. V., KUMAR, Manish |
| Předmět: |
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| Zdroj: |
Publications of the Research Institute for Mathematical Sciences; 2024, Vol. 60 Issue 3, p507-537, 31p |
| Abstrakt: |
A subalgebra A of a C*-algebra M is logmodular (resp. has factorization) if the set {a*a; a ∈M is invertible with a, a--1 ∈ A} is dense in (resp. equal to) the set of all positive and invertible elements of M. In this paper, we show that the lattice of projections in a (separable) von Neumann algebra M whose ranges are invariant under a logmodular algebra in M, is a commutative subspace lattice. Further, if M is a factor then this lattice is a nest. As a special case, it follows that all reflexive (in particular, completely distributive CSL) logmodular subalgebras of type I factors are nest algebras, thus answering in the affirmative a question by Paulsen and Raghupathi (Trans. Amer. Math. Soc. 363 (2011) 2627-2640). We also give a complete characterization of logmodular subalgebras in finite-dimensional von Neumann algebras. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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