JournalsrmiVol. 29, No. 4pp. 1373–1395

Normalisers of operator algebras and tensor product formulas

  • Martin McGarvey

    Queen's University Belfast, Belfast, Northern Ireland, UK
  • Lina Oliveira

    Instituto Superior Técnico, Lisboa, Portugal
  • Ivan G. Todorov

    Queen's University Belfast, Belfast, Northern Ireland, UK
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Abstract

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

Cite this article

Martin McGarvey, Lina Oliveira, Ivan G. Todorov, Normalisers of operator algebras and tensor product formulas. Rev. Mat. Iberoam. 29 (2013), no. 4, pp. 1373–1395

DOI 10.4171/RMI/760