Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-24T06:05:22.691Z Has data issue: false hasContentIssue false
  • English
  • Français

Co-Rank of a Composition Operator

Published online by Cambridge University Press:  20 November 2018

David J. Harrington
David J. Harrington*
Affiliation:
Hughes Aircraft Company Space and Communications, Group P.O. Box 92919 Los Angeles, California, 90009 U.S.A.
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.

A composition operator CT on L2(X, Σ,m) is a bounded linear transformation induced by a mapping T : X → X via CTf = f∘ T.

If m has no atoms then the co-rank of CT (i.e., dim is either zero or infinite. As a corollary, when m has no atoms, CT is a Fredholm operator iff it is invertible.

Keywords

Primary 47B99Secondary 47B38Composition operatorco-rankFredholm operator
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 29 , Issue 1 , 01 March 1986 , pp. 33 - 36
Copyright
Copyright © Canadian Mathematical Society 1986

References

1. Dunford, N. and Schwartz, J. T., Linear Operators I, Interscience, New York, 1958.Google Scholar
2. Harrington, D.J. and Whitley, R., Seminormal Composition Operators, J. Operator Theory, 11 (1984), pp. 125–135.Google Scholar
3. Kumar, A., Fredholm Composition Operators, Proc. Amer. Math. Soc, 79 (1980), pp. 233–236.Google Scholar
4. Nordgren, E., Composition Operators, Hilbert Space Operators Proceedings 1977, Lecture Notes in Mathematics No. 693, Springer-Verlag, Berlin, 1978.Google Scholar
5. Ridge, W. C., Spectrum of a Composition Operator, Proc. Amer. Math. Soc, 37 (1973), pp. 121—127.Google Scholar
6. Whitley, R. J., Normal and Quasinormal Composition Operators, Proc. Amer. Math. Soc, 70 (1978), pp. 114–117.Google Scholar