Extended Eigenvalues and Eigenoperators of Some Weighted Shift Operators

Abstract

A complex number is called an extended eigenvalue for an operator on a Hilbert space H if there exists a nonzero operator such that: such is called an extended eigenoperator corresponding to. The goal of this paper is to calculate extended eigenvalues and extended eigenoperators for the weighted unilateral (Forward and Backward) shift operators. We also find an extended eigenvalues for weighted bilateral shift operator. Moreover, the closedness of extended eigenvalues for the weighted unilateral (Forward and Backward) shift operators under multiplication is proven.