ON n-*-PARANORMAL OPERATORS

Abstract

Abstract. A Hilbert space operator T ∈ B(H ) is said to be n- * -paranormal, T ∈ C(n) for short, if T * x n ≤ T n x x n−1 for allx ∈ H . We proved some properties of class C(n) and we proved an asymmetric Putnam-Fuglede theorem for n- * -paranormal. Also, we study some invariants of Weyl type theorems. Moreover, we will prove that a class n- * paranormal operator is finite and it remains invariant under compact perturbation and some orthogonality results will be given.

Representation and normality of $\ast$-paranormal absolutely norm attaining operators

“…Here we explore this question for * -paranormal operators. In [19], it is proved that a compact * -paranormal operator is normal. We want to replace the space of all compact operators by a bigger class of ANoperators and see what extra assumptions we require to get normality.…”

Some results on totally n-star-paranormal operators

“…This class of operators introduced and studied by K. Tanahashi and A. Uchiyama. The references [12,13,14] are among the various extensions of these classes of operators.…”