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