It has been known since the 1970s that the closure of the algebraic tensor product of maximal abelian self-adjoint C*-subalgebras (MASAs) of two C*-algebras is maximal abelian in the minimal C*-tensor product of the containing C*-algebras. It turns out that this only remains true for other C*-tensor products if one of the MASAs has the extension property for pure states in the unital case. If neither MASA has the extension property there are examples where their tensor product is not maximal abelian. These result have interesting connections with some long-standing open questions.
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Last updated 2 May 2008. This page was created and is maintained by Stephen Wills (s.wills@ucc.ie).