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

M. Frank; V. Manuilov; E. Troitsky

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

Operator Algebras 2010-01-08 v2 General Topology

Authors: M. Frank , V. Manuilov , E. Troitsky

Abstract

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 $\prod_k I_k$ .

Keywords

hilbert modules c*-algebras cuntz semigroup

Cite

@article{arxiv.0908.1414,
  title  = {A reflexivity criterion for Hilbert C*-modules over commutative C*-algebras},
  author = {M. Frank and V. Manuilov and E. Troitsky},
  journal= {arXiv preprint arXiv:0908.1414},
  year   = {2010}
}

Comments

9 pages