Normalisers of operator algebras and tensor product formulas | Zendy

Martin McGarvey | Zendy; Lina Oliveira | Zendy; Ivan G. Todorov | Zendy

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Normalisers of operator algebras and tensor product formulas

Author(s) -

Martin McGarvey,

Lina Oliveira,

Ivan G. Todorov

Publication year - 2013

Publication title -

revista matemática iberoamericana

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.569

H-Index - 52

eISSN - 2235-0616

pISSN - 0213-2230

DOI - 10.4171/rmi/760

Subject(s) - tensor product , tensor product of algebras , mathematics , pure mathematics , product (mathematics) , algebra over a field , tensor product of hilbert spaces , operator (biology) , cartesian tensor , tensor contraction , tensor density , mathematical analysis , tensor field , chemistry , geometry , exact solutions in general relativity , biochemistry , repressor , gene , transcription factor

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].

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