Normalisers of operator algebras and tensor product formulas

Martin McGarvey; Lina Oliveira; Ivan G. Todorov

doi:10.4171/RMI/760

Normalisers of operator algebras and tensor product formulas

Martin McGarvey, Lina Oliveira, Ivan G. Todorov

Research output: Contribution to journal › Article

2 Citations (Scopus)

Abstract

We establish a tensor product formula for bimodules over maximal abelian self-adjoint algebras and their supports. We use this formula to show that if AA is the tensor product of finitely many continuous nest algebras, BB is a CSL algebra and AA and BB have the same normaliser semigroup then either A=BA=B or A∗=BA∗=B. We show that the result does not hold without the assumption that the nests be continuous, answering in the negative a question previously raised in the literature.

Original language	English
Pages (from-to)	1373-1395
Journal	Revista Matematica Iberoamericana
Volume	29
Issue number	4
DOIs	https://doi.org/10.4171/RMI/760
Publication status	Published - 2013

Bibliographical note

This paper has been accepted for publication in Revista Matematica Iberoamericana and, according to correspondence with the Editors, will appear within 2013.

ASJC Scopus subject areas

Mathematics(all)

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AB - We establish a tensor product formula for bimodules over maximal abelian self-adjoint algebras and their supports. We use this formula to show that if AA is the tensor product of finitely many continuous nest algebras, BB is a CSL algebra and AA and BB have the same normaliser semigroup then either A=BA=B or A∗=BA∗=B. We show that the result does not hold without the assumption that the nests be continuous, answering in the negative a question previously raised in the literature.

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