Multivalued Linear Operator Equation $$A^{*}A = \lambda A^{n}$$

Abstract

The main goal of this paper is to provide a complete description of the operator solutions (eventually multivalued) of the (multivalued) operator equation $$A^{*}A = \lambda A^{n}$$ , where n is a positive integer, A is a closed multivalued linear operator (a closed linear relation) on a complex Hilbert space $${{\mathfrak {H}}}$$ and $$\lambda $$ is a complex number.