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In this paper we characterize self-adjoint and normal composition operators on Poisson weighted sequence spaces l²(λ). However, the main purpose of this paper is to determine explicit conditions on inducing map under which a composition operator admits a best normal approximation. We extend results of Tripathi and Lal [Antinormal composition operators on l², Tamkang J. Math. 39 (2008), 347-352] to characterize antinormal composition operators on l²(λ). [ABSTRACT FROM AUTHOR]

An operator T is called n-normal operator if TnT* = T*Tn and n-quasinormal operator if TnT*T = T*TTn. In this paper, the conditions under which composition operators and weighted composition operators become n-normal operators and n-quasinormal operators have been obtained in terms of Radon-Nikodym derivative hn. [ABSTRACT FROM AUTHOR]