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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Composition operator on $ l\sp{p}$ and its adjoint


Authors: R. K. Singh and B. S. Komal
Journal: Proc. Amer. Math. Soc. 70 (1978), 21-25
MSC: Primary 47B37
DOI: https://doi.org/10.1090/S0002-9939-1978-0487574-8
MathSciNet review: 0487574
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Abstract: A necessary and sufficient condition for the invertibility of a composition operator $ {C_\phi }$ on $ {l^p}$ is reported in this paper. The adjoint of $ {C_\phi }$ is computed in the case $ p = 2$. The necessary and sufficient conditions for unitary operators and co-isometries to be composition operators are also investigated. A study of invariant subspaces and reducing subspaces of $ {C_\phi }$ is also made.


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DOI: https://doi.org/10.1090/S0002-9939-1978-0487574-8
Keywords: Composition operator, invertible and unitary operators, isometry, co-isometry, adjoint, invariant and reducing subspaces
Article copyright: © Copyright 1978 American Mathematical Society