Composition Operators on Poisson Weighted Sequence Spaces

DILIP KUMAR, HARISH CHANDRA

Abstract


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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