On the Systems of Finite Weights on the Algebra of Bounded Operators and Corresponding Translation Invariant Measures
- 作者: Bikchentaev A.1, Sakbaev V.2
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隶属关系:
- N. I. Lobachevskii Institute of Mathematics and Mechanics
- Moscow Institute of Physics and Technology
- 期: 卷 40, 编号 8 (2019)
- 页面: 1039-1044
- 栏目: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/205155
- DOI: https://doi.org/10.1134/S1995080219080067
- ID: 205155
如何引用文章
详细
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.
作者简介
A. Bikchentaev
N. I. Lobachevskii Institute of Mathematics and Mechanics
编辑信件的主要联系方式.
Email: Airat.Bikchentaev@kpfu.ru
俄罗斯联邦, Kazan, Tatarstan, 420008
V. Sakbaev
Moscow Institute of Physics and Technology
编辑信件的主要联系方式.
Email: fumi2003@mail.ru
俄罗斯联邦, Dolgoprudniy, Moscow oblast, 141700