Composition operator on 𝑙^{𝑝} and its adjoint

Singh, R. K.; Komal, B. S.

doi:10.1090/S0002-9939-1978-0487574-8

Composition operator on $l^{p}$ and its adjoint
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by R. K. Singh and B. S. Komal PDF

Proc. Amer. Math. Soc. 70 (1978), 21-25 Request permission

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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