ИЗМЕРИМЫЕ РАССЛОЕНИЯ ЛИНЕЙНЫХ ОПЕРАТОРОВ И ИХ ПРИЛОЖЕНИЯ К ОПЕРАТОРНЫМ АЛГЕБРАМ И ДИФФЕРЕНЦИРОВАНИЯМ

Аннотация

Subject of the inquiry: Banach - Kantorovich module, C*-algebras, measurable Banach bundles, non commutative Arens algebras , derivation. Aim of the inquiry: the realization of C*-algebras over A0 as algebras of operators on a Hilbert - Kaplansky module and description of derivation of the algebras of locally measurable operators affiliated with von Neumann algebra and of its subalgebras. Method of inquiry: In the work methods of measurable banach Bundles, of functional analysis, of theory operator algebras are used. The results achieved and their novelty: It is proved that any cyclically compact operator on a Banach - Kantorovich module can be represented as a measurable bundle of compact operators; it is proved that every V -Fredholm operator can be represented as a measurable bundle of Fredholm operators; it is proved that every C*-algebras over A0 is isometrically *-isomorphic to a closed subalgebra of the algebra of all A0-bounded A0-linear operators on a Hilbert - Kaplansky module; a general form of derivations of the algebras of locally measurable operators affiliated with a von Neumann algebra is given; a complete description of derivations on the non commutative Arens algebras associated with von Neumann algebra and faithful normal semi-finite trace is obtained. Practical value: the work has a theoretical character. Degree of embed and economic effectivity: Results and methods introduced in the work can be used in special courses on functional analysis and theory of operator algebras. Sphere of usage: the measure theory, functional analysis, theory of operator algebras, mathematical physics.