New conditions for counteractivity of normality operators

Abstract

An interesting area in operator theory is the study of norm inequalities for Hilbert space operators. Many mathematicians have worked on this subject, for example in [2, 3 and 5]. On the other hand, contractive and normaloid operators have been considered separately by [1, 6, 7 and 8]. In this paper, we results on conditions for normaloidity and contractivity of Hilbert space operators. We begin by simple lemmas before we move to main results. Let be a complex Hilbert space with an inner product and the algebra of all bounded linear operators on . denotes the usual operator norm and Dom( ) denotes the domain of