Eigenvalues of Generalized Shift Operators Over \(\ell ^p(\tau )\) Spaces

Abstract

In this note for \(p\in [1,+\infty )\), nonzero cardinal number \(\tau \), and one-to-one self-map \(\varphi :\tau \rightarrow \tau \) , we compute all possible eigenvalues of generalized shift operator \(\sigma _{\varphi }\upharpoonright _{\ell ^p(\tau )}:\ell ^p(\tau )\rightarrow \ell ^p(\tau )\).