Paranormal operators and some operator equations

Abstract

Let a pair (A;B) of bounded linear operators acting on a Hilbert space
be a solution of the operator equations ABA = A2 and BAB = B2. When
A is a paranormal operator, we explore some behaviors of the operators AB,
BA, and B. In particular, if A or A is a polynomial root of paranormal
operators, we show that Weyl type theorems are satised for the operators
AB, BA, and B.