Revista Matemática Iberoamericana
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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. Iberoam. 29 (2013), 1373-1395. doi: 10.4171/RMI/760