29 research outputs found
On the Systems of Finite Weights on the Algebra of Bounded Operators and Corresponding Translation Invariant Measures
© 2019, Pleiades Publishing, Ltd. We describe the class of translation invariant measures on the algebra ℬ(ℋ) of bounded linear operators on a Hilbert space ℋ and some of its subalgebras. In order to achieve this we apply two steps. First we show that a total minimal system of finite weights on the operator algebra defines a family of rectangles in this algebra through construction of operator intervals. The second step is construction of a translation invariant measure on some subalgebras of algebra ℬ(ℋ) by the family of rectangles. The operator intervals in the Jordan algebra ℬ(ℋ)sa is investigated. We also obtain some new operator inequalities
On the Systems of Finite Weights on the Algebra of Bounded Operators and Corresponding Translation Invariant Measures
© 2019, Pleiades Publishing, Ltd. We describe the class of translation invariant measures on the algebra ℬ(ℋ) of bounded linear operators on a Hilbert space ℋ and some of its subalgebras. In order to achieve this we apply two steps. First we show that a total minimal system of finite weights on the operator algebra defines a family of rectangles in this algebra through construction of operator intervals. The second step is construction of a translation invariant measure on some subalgebras of algebra ℬ(ℋ) by the family of rectangles. The operator intervals in the Jordan algebra ℬ(ℋ)sa is investigated. We also obtain some new operator inequalities
On the averaging of random semigroups and their generators by using the Chernoff theorem
Analogues of Jacobi and Weyl Theorems for Infinite-Dimensional Tori
The generalization of Jacobi and Weyl theorems on the dynamics of oscillators
on an infinite dimensional tori is presented. As in the classical theorems by
Jacibi and Weyl on the linear flow on a finite dimensional torus conditions are
obtained for periodicity, nonwandering, ergodicity and transitivity on an
invariant torus of trajectories of an infinite system of oscillators. We study
the ergodicity of a measure on an invariant torus with respect to the flow of a
system of oscillators.Comment: 13 pages, 0 figure