A NOTE ON P-SYMMETRIC OPERATORS
S. Bouali, Mohamed Ech-Chad, A. Zouaki, Youssef Bouhafsi · International Journal of Pure and Apllied Mathematics · 2016
Let L(H) denote the algebra of operators on a complex infinite dimensional Hilbert space H into itself.In this paper, we study the class of operators A ∈ L(H) which satisfy the following property, AT = T A implies AT * = T * A for all T ∈ C1(H) (trace class operators).Such operators are called p-symmetric.We establish some basic properties on the class of p-symmetric operators.We obtain new results concerning the intersection of the closure of R(δA), the range of the derivation δA(X) = AX -XA, and the commutant {A} ′ of A. We introduce the class of essentially d-symmetric operators.Some open problems are also presented.