Banach Journal of Mathematical Analysis

Finite-dimensional Hilbert C*-modules

Ljiljana Arambasic, Damir Bakic, and Rajna Rajic

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Abstract

In this paper we obtain a characterization of finite-dimensional Hilbert C*-modules. It is known that those are the modules for which both underlying C*-algebras are finite-dimensional. We show that such modules can be described by a certain property of bounded sequences of their elements. It turns out that similar property leads to another characterization of Hilbert C*-modules over C*-algebras of compact operators.

Article information

Source
Banach J. Math. Anal., Volume 4, Number 2 (2010), 147-157.

Dates
First available in Project Euclid: 7 February 2011

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1297117249

Digital Object Identifier
doi:10.15352/bjma/1297117249

Mathematical Reviews number (MathSciNet)
MR2610886

Zentralblatt MATH identifier
1195.46059

Subjects
Primary: 46L08: $C^*$-modules
Secondary: 46L05: General theory of $C^*$-algebras 46C50: Generalizations of inner products (semi-inner products, partial inner products, etc.)

Keywords
C*-algebra Hilbert C*-module (weakly) compact operator finite-dimensional C*-algebra finite-dimensional Hilbert C*-module

Citation

Arambasic, Ljiljana; Bakic, Damir; Rajic, Rajna. Finite-dimensional Hilbert C*-modules. Banach J. Math. Anal. 4 (2010), no. 2, 147--157. doi:10.15352/bjma/1297117249. https://projecteuclid.org/euclid.bjma/1297117249


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References

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