Is there any nontrivial compact generalized shift operator on Hilbert spaces?

Fatemah Ayatollah Zadeh Shirazi, Fatemeh Ebrahimifar

In the following text for cardinal number $\tau >0$, and self--map $\phi :\tau \to \tau$ we show the generalized shift operator ${\sigma }_{\phi }({\ell }^2(\tau ))\subseteq {\ell }^2(\tau )$ (where $σ_φ((x_α)_{α<τ})=(x_{φ(α)…