Revista Matemática Iberoamericana


Full-Text PDF (336 KB) | Metadata | Table of Contents | RMI summary
Volume 29, Issue 4, 2013, pp. 1373–1395
DOI: 10.4171/RMI/760

Published online: 2013-12-15

Normalisers of operator algebras and tensor product formulas

Martin McGarvey[1], Lina Oliveira[2] and Ivan G. Todorov[3]

(1) Queen's University Belfast, Belfast, Northern Ireland, UK
(2) Instituto Superior Técnico, Lisboa, Portugal
(3) Queen's University Belfast, Belfast, Northern Ireland, UK

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 $\mathcal{A}$ is the tensor product of finitely many continuous nest algebras, $\mathcal{B}$ is a CSL algebra and $\mathcal{A}$ and $\mathcal{B}$ have the same normaliser semigroup then either $\mathcal{A} =\mathcal{B}$ or $\mathcal{ A}^* = \mathcal{B}$. 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.

Keywords: CSL algebra, masa-bimodule, nest algebra, normaliser

McGarvey Martin, Oliveira Lina, Todorov Ivan: Normalisers of operator algebras and tensor product formulas. Rev. Mat. Iberoamericana 29 (2013), 1373-1395. doi: 10.4171/RMI/760