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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.
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Abstract

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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

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