Common Spectral Properties of Linear Operators A and B such that ABA=A^{2} and BAB=B^{2}

Christoph Schmoeger

Let $A$ and $B$ be bounded linear operators
on a Banach space such that $ABA=A^2$ and $BAB=B^2$.
Then $A$ and $B$ have some spectral properties in common.
This situation is studied in the present paper.