Fredholm weighted composition operators between weighted lp spaces: A simple process point of view

Abstract

Abstract In this paper we analyze, from a mathematical point of view, a simple processes with input in l p ⁢ ( 𝐫 ) {l^{p}(\mathbf{r})} and output in l p ⁢ ( 𝐬 ) {l^{p}(\mathbf{s})} . We characterize the functions u : ℕ → ℂ {u:\mathbb{N}\to\mathbb{C}} and φ : ℕ → ℕ {\varphi:\mathbb{N}\to\mathbb{N}} which define weighted composition operators W φ , u {W_{\varphi,u}} having closed range when acting between two different weighted l p {l^{p}} spaces. We also analyze when this operator is upper or lower semi-Fredholm.