Composition Operators on Poisson Weighted Sequence Spaces



The aim of this paper is to foster interaction between operator theory and probability. In this paper, we introduce Poisson weighted sequence space $l^{p}({\lambda})\{ \ \lambda > 0, 1 \leq p \leq \infty\}$ and observe that it is a Banach space. Also find a necessary and  sufficient condition for composition transformation $C_{\phi}$ to be bounded. Then we pass to characterize null space and range space of composition operators. We establish a necessary and a sufficient condition for range space of $C_{\phi}$ to be closed. Further, we determine condition under which composition operator is injective or surjective. Finally, we report  an explicit expression for the adjoint operator $C^{*}_{\phi}$ of composition operators on Hilbert space $l^{2}(\lambda)$ and study the above mentioned properties for $C^{*}_{\phi}$ on $l^{2}(\lambda)$.

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