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Hilbert modules revisited: orthonormal bases and Hilbert-Schmidt operators

Published online by Cambridge University Press:  18 May 2009

M. Cabrera ,
J. Martínez  and
A. Rodríguez
M. Cabrera
Affiliation:
Departamento DE Analisis Matematico, Facultad De Ciencias, Universidad De Granada, 18071-Granada, Spain
J. Martínez
Affiliation:
Departamento DE Analisis Matematico, Facultad De Ciencias, Universidad De Granada, 18071-Granada, Spain
A. Rodríguez
Affiliation:
Departamento DE Analisis Matematico, Facultad De Ciencias, Universidad De Granada, 18071-Granada, Spain
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The concept of a Hilbert module (over an H*-algebra) arises as a generalization of that of a complex Hilbert space when the complex field is replaced by an (associative) H*-algebra with zero annihilator. P. P. Saworotnow [13] introduced Hilbert modules and extended to its context some classical theorems from the theory of Hilbert spaces, J. F. Smith [17] gave a complete structure theory for Hilbert modules, and G. R. Giellis [9] obtained a nice characteristization of Hilbert modules.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 37 , Issue 1 , January 1995 , pp. 45 - 54
Copyright
Copyright © Glasgow Mathematical Journal Trust 1995

References

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