A reflexivity criterion for Hilbert C*-modules over commutative C*-algebras

Details A reflexivity criterion for Hilbert C*-modules over commutative C*-algebras A reflexivity criterion for Hilbert C*-modules over commutative C*-algebras

2009-08-10

arxiv.org/abs/0908.1414v2

Mathematics

Operator Algebras

9 pages

Scientific paper

A C*-algebra $A$ is C*-reflexive if any countably generated Hilbert C*-module $M$ over $A$ is C*-reflexive, i.e. the second dual module $M''$ coincides with $M$. We show that a commutative C*-algebra $A$ is C*-reflexive if and only if for any sequence $I_k$ of disjoint non-zero C*-subalgebras, the canonical inclusion $\oplus_k I_k\subset A$ doesn't extend to an inclusion of $\prod_k I_k$.

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