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Compact composition operators

Published online by Cambridge University Press:  09 April 2009

R. K. Singh  and
Ashok Kumar
R. K. Singh
Affiliation:
Department of Mathematics University of JammuJammu-180001, India
Ashok Kumar
Affiliation:
Department of Mathematics University of JammuJammu-180001, India
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Abstract

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Let (Хζ,λ) be a σ-finite measure space, and let ϕ be a non-singular measurable transformation from X into itself. Then a composition transformation Cϕ on L2(λ) is defined by Cϕf = f ∘ ϕ. If Cϕ is a bounded operator, then it is called a composition operator. The space L2(λ) is said to admit compact composition operators if there exists a ϕ such that Cϕ is compact. This note is a report on the spaces which admit or which do not admit compact composition operators.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 28 , Issue 3 , November 1979 , pp. 309 - 314
Copyright
Copyright © Australian Mathematical Society 1979

References

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