Abstract In this paper we analyze, from a mathematical point of view, a simple processes with input in <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:msup> <m:mi>l</m:mi> <m:mi>p</m:mi> </m:msup> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>𝐫</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> </m:math> {l^{p}(\mathbf{r})} and output in <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:msup> <m:mi>l</m:mi> <m:mi>p</m:mi> </m:msup> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>𝐬</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> </m:math> {l^{p}(\mathbf{s})} . We characterize the functions <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>u</m:mi> <m:mo>:</m:mo> <m:mrow> <m:mi>ℕ</m:mi> <m:mo>→</m:mo> <m:mi>ℂ</m:mi> </m:mrow> </m:mrow> </m:math> {u:\mathbb{N}\to\mathbb{C}} and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>φ</m:mi> <m:mo>:</m:mo> <m:mrow> <m:mi>ℕ</m:mi> <m:mo>→</m:mo> <m:mi>ℕ</m:mi> </m:mrow> </m:mrow> </m:math> {\varphi:\mathbb{N}\to\mathbb{N}} which define weighted composition operators <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mi>W</m:mi> <m:mrow> <m:mi>φ</m:mi> <m:mo>,</m:mo> <m:mi>u</m:mi> </m:mrow> </m:msub> </m:math> {W_{\varphi,u}} having closed range when acting between two different weighted <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mi>l</m:mi> <m:mi>p</m:mi> </m:msup> </m:math> {l^{p}} spaces. We also analyze when this operator is upper or lower semi-Fredholm.