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 › peer-review

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

General Mathematics

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Cite this

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AU - Todorov, Ivan G.

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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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DO - 10.4171/RMI/760

M3 - Article

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JF - Revista Matematica Iberoamericana

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Normalisers of operator algebras and tensor product formulas

Abstract

Bibliographical note

ASJC Scopus subject areas

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