TAILIEUCHUNG - Báo cáo toán học: "Nest-subalgebras of von Neumann algebras: Commutants modulo the Jacobson radical "

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Journal of Operator Theory đề tài: Yến-subalgebras của von Neumann đại số: modulo thể chuyển đổi các cấp tiến Jacobson. | Copyright by INCREST 1985 J. OPERATOR THEORY 10 1983 95 118 NEST-SUBALGEBRAS OF VON NEUMANN ALGEBRAS COMMUTANTS MODULO THE JACOBSON RADICAL FRANK GILFEATHER and DAVID R. LARSON This paper is a sequel to 10 and 11 in which properties of the class of nest subalgebras of von Neumann algebras have been systematically explored. A nest subalgebra of a von Neumann algebra nsva is an operator algebra of the form n alg where Ổ is a von Neumann algebra and jV is a nest of projections in ổỹ. These algebras which are natural generalizations of Ringrose s nest algebras 25 are closely related to other classes of nonselfadjoint algebras which have been extensively studied most notably the triangular algebras 16 the subdiagonal algebras 1 and the algebras of analytic operators 20 . In 10 some basic properties of an nsva were given. The main structure results given there include a central decomposition into a direct integral of nest subalgebras of factor von Neumann algebras and a characterization of the Jacobson radical of an nsva which is the natural generalization of the characterization of the radical of a nest algebra given by Ringrose 25 . Subsequently in 11 the essential commutant commutant modulo the compact operators of an nsva was determined extending the result for von Neumann algebras due to Johnson and Parrot 15 and a result for nest algebras due to Christensen and Peligrad 4 In addition some results concerning the Arveson distance estimate for a nsva and other algebras were obtained in 11 . The structure of the invariant subspace lattice of a nsva was studied in 10 . In this paper we consider structural properties related to the radical. We use the term ăi-commutant of the core to denote the set of operators in an nsva si which commute with the core modulo the radical and the term -center will denote the set of operators in that commute modulo the radical with every element of s . Here core denotes the von Neumann algebra generated by the nest and the central .

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