Some Properties of (M, k)−Quasi Paranormal Operators on Hilbert Spaces.

Let H be a complex Hilbert space and let T represent a bounded linear operator on H. In this paper we introduce, a new class of non normal operators, the (M, k)-quasi paranormal operator. An operator T is said to be a (M,k)-quasi paranormal operator, for a non negative integer k and a real positive number M if it satisfies ||Tk+1x||2 < M||Tk+2x|| ||Tkx||, for all x ∈ H. This new class of operators is generalization of some of the non normal operators, such as, the k-quasi paranormal and M-paranormal operators. We prove the basic properties, the structural and spectral properties and also the matrix representation of this new class of operators. [ABSTRACT FROM AUTHOR]