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Composition operators on a functional Hilbert space

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, Tawi, India.
S.D. Sharma
Affiliation:
Department of Mathematics, University of Jammu, Jammu, Tawi, India.
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Abstract

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Let T be a mapping from a set X into itself and let H(X) be a functional Hilbert space on the set X. Then the composition operator CT on H(X) induced by T is a bounded linear transformation from H(X) into itself defined by CTf = f ∘ T. In this paper composition operators are characterized in the case when H(X) = H2(π+) in terms of the behaviour of the inducing functions in the vicinity of the point at infinity. An estimate for the lower bound of ∥CT∥ is given. Also the invertibility of CT is characterized in terms of the invertibility of T.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 20 , Issue 3 , June 1979 , pp. 377 - 384
Copyright
Copyright © Australian Mathematical Society 1979

References

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