Some Properties of (M,k)-quasi Paranormal Operators on Hilbert Spaces (European Journal of Pure and Applied Mathematics, 2024)
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 (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 every x in H.This new class of operators is a 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.
Keywords: (M,k)-quasi paranormal operator; M-quasi paranormal operator; k-quasi paranormal operator; M- paranormal operator; approximate point spectrum of operator