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Normal and invertible composition operators

Published online by Cambridge University Press:  17 April 2009

R.K. Singh  and
D.K. Gupta
R.K. Singh
Affiliation:
Department of Mathematics, University of Jarmiu, Jammu, India.
D.K. Gupta
Affiliation:
Department of Mathematics, University of Jarmiu, Jammu, India.
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Let N denote the set of natural numbers and let φ be a mapping from N into itself. Then the composition transformmation Cφ, on the weighted l2 space with weights a2n, where n ∈ N and 0 < a < 1 is defined by Cφf = f ∘ φ. If Cφ is a bounded operator, then it is called a composition operator. The adjoint of the composition operator Cφ, is computed, and it is used to characterise normal, unitary, isometric, and co-isometric composition operators. Not every invertible φ induces an invertible composition operator, as is shown by examples. At the end of this note all invertible composition operators are characterised.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 18 , Issue 1 , February 1978 , pp. 45 - 54
Copyright
Copyright © Australian Mathematical Society 1978

References

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