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Subjects
46-XX Functional analysis
46Lxx Selfadjoint operator algebras ( $C^{*}$ -algebras, von Neumann ( $W^{*}$ -) algebras, etc.)
46L06 Tensor products of $C^{*}$ -algebras

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Conditions equivalent to C* independence

Shuilin Jin, Li Xu, Qinghua Jiang, Li Li (2012)

Studia Mathematica

Let and be mutually commuting unital C* subalgebras of (). It is shown that and are C* independent if and only if for all natural numbers n, m, for all n-tuples A = (A₁, ..., Aₙ) of doubly commuting nonzero operators of and m-tuples B = (B₁, ..., Bₘ) of doubly commuting nonzero operators of , $S p (A, B) = S p (A) \times S p (B)$ , where Sp denotes the joint Taylor spectrum.

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