Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2025-01-03T18:22:36.989Z Has data issue: false hasContentIssue false
  • English
  • Français

Non-compact composition operators

Published online by Cambridge University Press:  17 April 2009

R.K. Singh  and
S.D. Sharma
R.K. Singh
Affiliation:
Department of Mathematics, University of Jammu, Jammu 180001, India.
S.D. Sharma
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.

In this note sufficient conditions for non-compactness of composition operators on two different functional Hilbert spaces have been obtained.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 21 , Issue 1 , February 1980 , pp. 125 - 130
Copyright
Copyright © Australian Mathematical Society 1980

References

[1]Carathéodory, C., Theory of functions of a complex variable, Volume two (translated by Steinhardt, F.. Chelsea, New York, 1960).Google Scholar
[2]Nordgren, Eric A., “Composition operators on Hilbert spaces”, Hilbert space operators, 37–63 (Proc. Conf. Hilbert Space Operators, California State University, Long Beach, 1977. Lecture Notes in Mathematics, 693. Springer-Verlag, Berlin, Heidelberg, New York, 1978).CrossRefGoogle Scholar
[3]Shapiro, J.H. & Taylor, P.D., “Compact, nuclear, and Hilbert-Schmidt composition operators on H 2”, Indiana Univ. Math. J. 23 (1973), 471–496.CrossRefGoogle Scholar
[4]Singh, R.K., “A relation between composition operators on H 2(D) and H 2(Π+)”, Pure and Appl. Math. Sci. 1 (1974/1975), no. 2, 1–5.Google Scholar
[5]Singh, R.K. and Sharma, S.D., “Composition operators on a functional Hilbert space”, Bull. Austral. Math. Soc. 20 (1979), 377–384.CrossRefGoogle Scholar
[6]Swanton, Donald Wesley, “Composition operators on HP(D)” (PhD thesis, Northwestern University, Evanston, Illinois, 1974)Google Scholar