Compact and quasinormal composition operators
Author: Raj Kishor Singh
Journal: Proc. Amer. Math. Soc. 45 (1974), 80-82
MSC: Primary 47B37
MathSciNet review: 0348545
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Abstract: Let be a composition operator on , where is a -finite measure on a set . If is nonatomic, then Ridge proved that no one-to-one composition operator , with dense range is compact. This result is generalized in the paper by removing one-to-one and dense range conditions. The quasinormal composition operators are also characterized in terms of commutativity with the multiplication operator induced by the Radon-Nikodym derivative of the measure with respect to .
-  W. C. Ridge, Composition operators, Thesis, Indiana University, 1969.
-  R. K. Singh, Composition operators (to appear).
-  Adriaan Cornelis Zaanen, Integration, North-Holland Publishing Co., Amsterdam; Interscience Publishers John Wiley & Sons, Inc., New York, 1967. Completely revised edition of An introduction to the theory of integration. MR 0222234
- W. C. Ridge, Composition operators, Thesis, Indiana University, 1969.
- R. K. Singh, Composition operators (to appear).
- A. C. Zaanen, Integration, Completely revised edition of An introduction to the theory of integration, North-Holland, Amsterdam, Interscience, New York, 1967. MR 36 #5286. MR 0222234 (36:5286)
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Keywords: Composition operators, compact operators, quasinormal composition operators, atomic measures, nonatomic measures
Article copyright: © Copyright 1974 American Mathematical Society