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Vestnik Samarskogo Universiteta. Estestvenno-Nauchnaya Seriya, 2022, Volume 28, Issue 1-2, Pages 23–31
DOI: https://doi.org/10.18287/2541-7525-2022-28-1-2-23-31
(Mi vsgu674)
 

Mathematics

How the distance between subspaces in the metric of a spherical opening affects the geometric structure of a symmetric space

S. I. Strakhov

Samara National Research University, Samara, Russian Federation (published under the terms of the Creative Commons Attribution 4.0 International License)
References:
Abstract: A relationship is found between the metric of a spherical opening on the space of all subspaces of a symmetric space and some numerical characteristic of the subspace. It is known that, for example, in $L_1$ this characteristic takes only two values (i.e. this is a binary space), while in $L_2$ there are infinitely many values. Using the connection found, the necessary conditions for the binarity of a symmetric space were generalized.
Keywords: symmetric space, Orlicz space, spherical opening between subspaces, disjoint functions, independent functions, strongly embedded subspace.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-02-2022-878
The work was completed as a part of the implementation of the development program of the Scientific and Educational Mathematical Center the Volga Federal District, agreement no. 075-02-2022-878.
Received: 30.08.2022
Revised: 05.10.2022
Accepted: 14.11.2022
Document Type: Article
UDC: 517.982.22
Language: Russian
Citation: S. I. Strakhov, “How the distance between subspaces in the metric of a spherical opening affects the geometric structure of a symmetric space”, Vestnik SamU. Estestvenno-Nauchnaya Ser., 28:1-2 (2022), 23–31
Citation in format AMSBIB
\Bibitem{Str22}
\by S.~I.~Strakhov
\paper How the distance between subspaces in the metric of a spherical opening affects the geometric structure of a symmetric space
\jour Vestnik SamU. Estestvenno-Nauchnaya Ser.
\yr 2022
\vol 28
\issue 1-2
\pages 23--31
\mathnet{http://mi.mathnet.ru/vsgu674}
\crossref{https://doi.org/10.18287/2541-7525-2022-28-1-2-23-31}
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    Вестник Самарского государственного университета. Естественнонаучная серия
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