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

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