Abstract
The purpose of this paper is to obtain structural properties for a class of linear operators on semi-Hilbertian spaces i.e., spaces generated by positive semi-definite sesquilinear forms. This kind of spaces appears in many problems concerning linear and bounded operators on Hilbert spaces and is intensively studied in the present. We call the elements of this class A-paranormal operators. An operator T is an element of B(H) is said to be A-paranormal if parallel to Tx parallel to(2)(A) <= parallel to T(2)x parallel to(A), for all x is an element of H : parallel to x parallel to(A) = 1. Some of the basic properties of this class are studied. Moreover, the product, tensor product and the sum of finite numbers of these type are discussed.