Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2025-01-03T18:53:15.896Z Has data issue: false hasContentIssue false
  • English
  • Français

Atomic measure spaces and essentially normal composition operators

Published online by Cambridge University Press:  17 April 2009

R.K. Singh  and
T. Veluchamy
R.K. Singh
Affiliation:
Department of Mathematics, University of Jammu, Jammu 180001, India.
T. Veluchamy
Affiliation:
Department of Mathematics, University of Jammu, Jammu 180001, India.
Rights & Permissions [Opens in a new window]

Abstract

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 adjoint of a composition operator CT on the L2-space of an atomic measure is computed and a characterization for an operator to be a composition operator is given in this short note. The dimensions of kernel and co-kernel of CT are calculated in order to characterise Fredholm composition operators. Finally, essentially normal composition operators are studied on l2.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 27 , Issue 2 , April 1983 , pp. 259 - 267
Copyright
Copyright © Australian Mathematical Society 1983

References

[1]Douglas, Ronald G., Banaoh algebra techniques in operator theory (Pure and Applied Mathematics, 49. Academic Press, New York, London, 1972).Google Scholar
[2]Kumar, Ashok, “Fredholm composition operators”, Proc. Amer. Math. Soc. 79 (1980), 233–236.CrossRefGoogle Scholar
[3]Nordgren, Eric A., “Composition operators on Hilbert spaces”, Hilbert space operators, 37–63 (Proc. Conf. Long Beach, California, 1977. Lecture Notes in Mathematics, 693. Springer-Verlag, Berlin, Heidelberg, New York, 1978).CrossRefGoogle Scholar
[4]Singh, R.K. and Komal, B.S., “Composition operators on lp and its adjoint”, Proc. Amer. Math. Soc. 70 (1978), 21–25.Google Scholar
[5]Singh, R.K. and Kumar, Ashok, “Characterizations of invertible, unitary, and normal composition operators”, Bull. Austral. Math. Soc. 19 (1978), 81–95.CrossRefGoogle Scholar
[6]Whitley, Robert, “Normal and quasinormal composition operators”, Proc. Amer. Math. Soc. 70 (1978), 114–118.CrossRefGoogle Scholar
[7]Zannen, A.C., Integration (North Holland, Amsterdam; Interscience, New York, 1967).Google Scholar