Author:
Bouhafsi Youssef,Ech-chad Mohamed,Zouaki Adil
Abstract
Let H be a separable infinite dimensional complex Hilbert space, and let L(H) denote the algebra of all bounded linear operators on H into itself. Given A, B ∈ L(H), define the generalized derivation δA, B ∈ L(L(H)) by δA, B(X) = AX - XB. An operator A ∈ L(H) is P-symmetric if AT = TA implies AT* = T* A for all T ∈ C1(H) (trace class operators). In this paper, we give a generalization of P-symmetric operators. We initiate the study of the pairs (A, B) of operators A, B ∈ L(H) such that R(δA, B) W* = R(δA, B) W*, where R(δA, B) W* denotes the ultraweak closure of the range of δA, B. Such pairs of operators are called generalized P-symmetric. We establish a characterization of those pairs of operators. Related properties of P-symmetric operators are also given.
Publisher
Universidad Nacional de Colombia
Reference14 articles.
1. J. H. Anderson, J. W. Bunce, J. A. Deddens, and J. P. Williams, C*-algebras and derivation ranges, Acta Sci. Math. (Szeged) 40 (1978), no. 3-4, 211-227.
2. C. A. Bergerand and B. I. Shaw, Self-commutators of multicyclic hyponormal operators are always trace class, Bull. Amer. Math. Soc. 79 (1973), 1193-1199.
3. S. Bouali and Y. Bouhafsi, On the range-kernel orthogonality and p-symmetric operators, Math. Inequal. Appl. 9 (2006), no. 3, 511-519.
4. S. Bouali and Y. Bouhafsi, P-symmetric operators and the range of a subnormal derivation, Acta Sci. Math(Szeged) 72 (2006), no. 3-4, 701-708.
5. S. Bouali and J. Charles, Extension de la notion d'opérateur D-symétrique I, Acta Sci. Math. (Szeged) 51 (1993), no. 1-4, 517-525.