Hostname: page-component-848d4c4894-pftt2 Total loading time: 0 Render date: 2024-05-03T08:27:14.335Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

REFERENCES

1.Allison, B. N., Models of isotropic simple Lie algebras, Comm. Algebra 7 (1979), 1835–1875.CrossRefGoogle Scholar
2.Ambrose, W., Structure theorems for a special class of Banach algebras, Trans. Amer. Math. Soc. 57 (1945), 364–386.CrossRefGoogle Scholar
3.Bonsall, F. F. and Duncan, J., Complete normed algebras (Springer-Verlag, 1973).CrossRefGoogle Scholar
4.Cabrera, M., Marrakchi, A. El, Martínez, J. and Rodríguez, A., An Allison-Kantor-Koecher-Tits construction for Lie H*-algebras, J. Algebra 164 (1994), 361–408.CrossRefGoogle Scholar
5.Cabrera, M., Marrakchi, A. El, Martínez, J. and Rodríguez, A., Bounded differential operators on Hilbert modules and derivations of structurable H*-algebras, Commun. Algebra 21 (1993), 2905–2945.CrossRefGoogle Scholar
6.Cabrera, M., Martínez, J. and Rodríguez, A., Structurable H*-algebras, J. Algebra 47 (1992), 19–62.CrossRefGoogle Scholar
7.Cuenca, J. A. and Rodríguez, A., Structure theory for noncommutative Jordan H*-algebras, J. Algebra 106 (1987), 1–14.Google Scholar
8.Choquet, G., Topologie. Cours D'Analyse, Tome II (Masson et C, 1969).Google Scholar
9.Giellis, G. R., A characterization of Hilbert modules, Proc. Amer. Math. Soc. 36 (1972), 440–442.CrossRefGoogle Scholar
10.Jacobson, N., Structure of rings. American Mathematical Society Colloquium Publication, Vol. 37. (Providence, R.I., 1968).Google Scholar
11.Rickart, E., General theory of Banach algebras (Krieger Publishing Company, New York, 1970).Google Scholar
12.Rodríguez, A., Contribución a la Teoría de las C*-algebras con unidad. Tesis Doctoral (Secretariado de Publicaciones de la Universidad de Granada, 1974).Google Scholar
13.Saworotnow, P. P., A generalized Hilbert space, Duke Math. J. 35 (1968), 191–197.CrossRefGoogle Scholar
14.Saworotnow, P. P., Trace-class and centralizers of an H*-algebra, Proc. Amer. Math. Soc. 26 (1970), 101–104.Google Scholar
15.Saworotnow, P. P. and Friedell, J. C., Trace-class for arbitrary H*-algebras, Proc. Amer. Math. Soc. 26 (1970), 95–100.Google Scholar
16.Schatten, R., Norm ideals of completely continuous operators (Springer-Verlag, 1970).CrossRefGoogle Scholar
17.Smith, J. F., The structure of Hilbert modules, J. London Math. Soc. 8 (1974), 741–749.CrossRefGoogle Scholar