Common Properties Of Operators SR And RS And W-hyponormal Operators

This paper mainly studies the relations between operators SRand RSacting on a Banach space, the spectral structure of w-hyponormal operators on a Hilbert space and generalized Weyl's theorem. There are three chapters in the paper. Chapter 1 mainly introduces some basic results, including some conceptions and notations needed in the following chapters. In chapter 2, we discuss the B - Fredholm, B -Weyl spectral and Drazin inverse properties common to SRand RS. In chapter 3. we prove that p-hyponormal operators and log-hyponormal operators satisfy generalizedWeyl's theorem. We discuss the spectral structure of w-hyponormal operator T, and prove that T with ker(T) (?) ker(T*) satisfies generalized Weyl's theorem.