m-QUASI-(n;A)-PARANORMAL OPERATORS IN SEMI-HILBERTIAN SPACES
Abstract
The study of semi-Hilbert spaces operators is motivated by what
are called pseudo-Hermitian quantum mechanics. In this paper, we introduce
the concept of m-quasi-n-paranormal of a bounded linear operators on a complex
Hilbert space with a semi-inner product induced by a positive operator A.
This generalizes the classical m-quasi-n-paranormality of operators on Hilbert
spaces to semi-Hilbert space. We investigate some basic properties of this new
class. Product and tensor product results were also investigated.
Keywords
A-adjoint, Semi-Hilbertian spaces, A-positive operators, Paranormal operators, Quasi-paranormal operators.