Kazan (Volga region) Federal University, KFU
KAZAN
FEDERAL UNIVERSITY
 
ON THE SYSTEMS OF FINITE WEIGHTS ON THE ALGEBRA OF BOUNDED OPERATORS AND CORRESPONDING TRANSLATION INVARIANT MEASURES
Form of presentationArticles in international journals and collections
Year of publication2019
Языканглийский
  • Bikchentaev Ayrat Midkhatovich, author
  • Sakbaev Vsevolod Zhanovich, author
  • Bibliographic description in the original language A. M. Bikchentaev, OV. Zh. Sakbaev, On the systems of finite weights on the algebra of bounded operators and corresponding translation invariant measures //Lobachevskii Journal of Mathematics, 2019, Vol. 40, No. 8, pp. 1039–1044
    Annotation 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.
    Keywords Hilbert space, projection, operator interval, Jordan algebra, translation invariant measure, trace, Hilbert?Schmidt operator, operator inequality, convexity
    The name of the journal Lobachevskii Journal of Mathematics
    On-line resource for training course http://dspace.kpfu.ru/xmlui/bitstream/handle/net/151737/F_LOJM1039.pdf?sequence=1&isAllowed=y
    Please use this ID to quote from or refer to the card https://repository.kpfu.ru/eng/?p_id=206282&p_lang=2
    Resource files 
    File name Size (MB) Format  
    F_LOJM1039.pdf 0,51 pdf show / download

    Full metadata record