On operators satisfying T*| T| T ≥ T*| T*| T.

Let T be a bounded linear operator on a complex Hilbert space H. In this paper we introduce a new class denoted by l-*- A, of operators satisfying T*| T| T ≥ T*| T*| T, and we prove the basic properties of these operators. Using these results, we also prove that if T or T* ∈ l-*- A, then w( f( T)) = f( w( T)), σ( f( T)) = f( σ( T)) for every f ∈ H( σ( T)), where H( σ( T)) denotes the set of all analytic functions on an open neighborhood of σ( T). [ABSTRACT FROM AUTHOR]