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Normal and quasinormal weighted composition operators

Published online by Cambridge University Press:  18 May 2009

James T. Campbell,
Mary Embry-Wardrop,
Richard J. Fleming and
S. K. Narayan
James T. Campbell
Affiliation:
Department of Mathematical Sciences, Memphis State University, Memphis, TN. 38152, U.S.A.
Mary Embry-Wardrop
Affiliation:
Department of Mathematics, Central Michigan University, Mt. Pleasant, Michigan 48859, U. S. A.
Richard J. Fleming
Affiliation:
Department of Mathematics, Central Michigan University, Mt. Pleasant, Michigan 48859, U. S. A.
S. K. Narayan
Affiliation:
Department of Mathematics, Central Michigan University, Mt. Pleasant, Michigan 48859, U. S. A.
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In their paper [1], Campbell and Jamison attempted to give necessary and sufficient conditions for a weighted composition operator on an L2 space to be normal, and to be quasinormal. Those conditions, specifically Theorems I and II of that paper, are not valid (see [2] for precise comments on the other results in that paper). In this paper we present a counterexample to those theorems and state and prove characterizations of quasinormality (Theorem 1 below) and normality (Theorem 2 and Corollary 3 below). We also discuss additional examples and information concerning normal weighted composition operators which contribute to the further understanding of this class.

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 33 , Issue 3 , September 1991, pp. 275 - 279
Copyright
Copyright © Glasgow Mathematical Journal Trust 1991

References

REFERENCES

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3.Foguel, S., The ergodic theory of Markov processes, Math. Studies No. 21 (Van Nostrand Reinhold, New York, 1969).Google Scholar
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