Product of powers of quasinormal composition operators

[T.sub.i], i = 1, 2 be measurable transformations which define bounded composition operators [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] on [L.sup.2] of a [sigma]-finite measure space. Denote their respective Radon-Nikodym derivatives by [h.sub.i], i = 1,2. The main result of the paper is th...

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Bibliographic Details
Published in:Scientia magna 2009-09, Vol.5 (3), p.56-56
Main Authors: Thirugnanasambandam, K, Panayappan, S
Format: Article
Language:English
Subjects:
Mathematics
Operator theory
Transformations (Mathematics)
Online Access:Get full text
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Summary:[T.sub.i], i = 1, 2 be measurable transformations which define bounded composition operators [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] on [L.sup.2] of a [sigma]-finite measure space. Denote their respective Radon-Nikodym derivatives by [h.sub.i], i = 1,2. The main result of the paper is that, if [h.sub.i] * [T.sub.i] = [h.sub.j] a.e., for i,j = 1, 2, then for each of the positive integers m,n,p the operators [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are quasinormal. As a consequence, we see that the sufficient condition established in our paper [5] for quasinormality of a composition operator is actually sufficient for all powers to be quasinormal. Keywords Quasinormal operators, powers of quasinormal composition operators.
ISSN:1556-6706