A characterization of Hilbert $C^*$-modules over finite dimensional $C^*$-algebras

Details A characterization of Hilbert $C^*$-modules over finite dimensional $C^*$-algebras A characterization of Hilbert $C^*$-modules over finite dimensional $C^*$-algebras

2008-12-04

arxiv.org/abs/0812.0889v1

Oper. Matrices 3 (2009), no. 2, 235-240

Mathematics

Operator Algebras

7 Pages; to appear in Operators and Matrices (OAM)

Scientific paper

We show that the unit ball of a full Hilbert $C^*$-module is sequentially
compact in a certain weak topology if and only if the underlying $C^*$-algebra
is finite dimensional. This provides an answer to the question posed in J.
Chmieli\'nski et al [Perturbation of the Wigner equation in inner product
$C^*$-modules, J. Math. Phys. 49 (2008), no. 3, 033519; arXiv:0801.2726].

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