Totaly *-paranormal and the Operators Equations SRS= S2 and RSR= R2

Buthainah A.A. Ahmed, Hassan N. Almrayatee

Abstract: In this paper we study the property of the operator equations SRS = S2 and RSR = R2 where S is a *-paranormal operator we show that if S or S is a polynomial root of *-paranormal operator then f (A) 2 gW for all f 2 H ( (A)), where A 2 fAB, BA, Bg and we show that For the operator equation SRS = S2 and RSR = R2 we have  (S) =  (SR) =  (RS) =  (R)

Keywords: Paranormal operator, generalized Weyls theorem, single valued extension property