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Composition Operators

Published online by Cambridge University Press:  20 November 2018

Eric A. Nordgren
Eric A. Nordgren*
Affiliation:
University of New Hampshire, Durham, N.H.
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The object of this note is to report on some of the properties of a class of operators induced by inner functions. If m is normalized Lebesgue measure on the unit circle X in the complex plane and C ϕ is an inner function (a complex function on X of unit modulus almost everywhere whose Poisson integral is a non-constant holomorphic function in the open unit disk), then an operator C ϕ on L 2(m) is defined by

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968, pp. 442 - 449
Copyright
Copyright © Canadian Mathematical Society 1968

Footnotes

Work supported in part by a grant from the National Science Foundation.

References

1. Brown, A., On a class of operators, Proc. Amer. Math. Soc, 4 (1953), 723–728.Google Scholar
2. Ford, L. R., Automorphic functions (New York, 1929).Google Scholar
3. Halmos, P. R., Shifts on Hilbert spaces, J. Reine Angew. Math., 208 (1961), 102–112.Google Scholar
4. Hoffman, K., Banach spaces of analytic functions (Englewood Cliffs, N.J., 1962).Google Scholar