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 is the tensor product of finitely many continuous nest algebras, is a CSL algebra and and have the same normaliser semigroup then either or . 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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Martin McGarvey, Lina Oliveira, Ivan G. Todorov, Normalisers of operator algebras and tensor product formulas. Rev. Mat. Iberoam. 29 (2013), no. 4, pp. 1373–1395DOI 10.4171/RMI/760