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We establish a tensor product formula for bimodules over maximal abelian selfadjoint algebras and their supports. We use this formula to show that if A is the tensor product of finitely many continuous nest algebras, B is a CSL algebra and A and B have the same normaliser semi-group then either A = B or A∗ = B. We show that the result does not hold without the assumption that the nests be continuous, answering in the negative a question raised in [28].

Normalisers of operator algebras and tensor product formulas