On spectral properties of -commuting operators in Hilbert spaces

Abstract

Let B(H) denote the Banach algebra of bounded linear operators on a complex Hilbert space H and let A;B 2 B(H) satisfying the equation; AB = BA; 2 C;AB 6= 0, where C denotes the complex number eld. In this case A and B are said to be -commuting operators. In this paper we investigate the conditions under which either AB and BA or B and B have same spectrum or same essential spectrum.