On M−quasi Paranormal Operators

Abstract

In this paper we introduce a new class of operators called M−quasi paranormal operators. A bounded linear operator T in a complex Hilbert space H is said to be a M−quasi paranormal operator if it satisfies ∥T 2x∥ 2 ≤ M∥T 3x∥ · ∥T x∥, ∀x ∈ H, where M is a real positive number. We prove basic properties, the structural and spectral properties of this class of operators.