On eigenvalues of generalized shift linear vector isomorphisms

Abstract

Our main aim is to compute eigenvalues<br />of generalized shift isomorphism $sigma_varphi:V^Gammato<br />V^Gamma$ with $sigma_varphi((x_alpha)_{alphainGamma})=<br />(x_{varphi(alpha)})_{alphainGamma}$ ($<br />(x_alpha)_{alphainGamma}in V^Gamma$) where $V$ is a<br />vector space (over field $F$), $Gamma$ is a nonempty arbitrary set and $varphi:GammatoGamma$ is an arbitrary bijection.