Локальлные дифференцирования на алгебрах измеримых операторов

Аннотация

Subjects of inquiry: Algebra of measurable operators, non commutative Arens algebras, local derivations. Aim of the inquire: Description of local derivations on algebras of measurable operators. Methods of the inquire: In the work general methods of functional analysis, of theory operator algebras are used. The results achieved and their novelty: a description of local derivations on the non commutative Arens algebras associated with von Neumann algebra and faithful normal semi-finite trace is obtained; it is proved that every tT-continuous linear operator Д on the algebra 5(Л/,т) satisfying the identity A(p) = A(p)/? + /?A(p) is a derivation, where AY be a von Neumann algebra with a faithful normal semi-finite trace r; it is proved that every linear operator D: 4(X) —> B(X) satisfying the identity Z)(x") = У^хА 'D(x)x"~*, хбЛ(Т) *=i is a spatial derivation, where n > 3 - some fix number; necessary and sufficient conditions for the existence of local derivations which are not derivations on algebras S(M) and S(M,r) affiliated with a commutative von Neumann algebra are obtained; a description of local derivations of the algebras LS(M), S(M) and S(M,r) concerning type I von Neumann algebras without abelian direct summands is obtained. Practical value: The results of the dissertation have a theoretical character. Degree of embed and economic effectivity: The results, presented in the work can be used in special courses on functional analysis and theory of operator algebras for masters and post-graduate students. Field of application: Functional analysis, theory of operator algebras, mathematical physics and its applications.