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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)
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.
Received: 30.08.2022 Revised: 05.10.2022 Accepted: 14.11.2022
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
Linking options:
https://www.mathnet.ru/eng/vsgu674 https://www.mathnet.ru/eng/vsgu/v28/i1/p23
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Abstract page: | 67 | Full-text PDF : | 22 | References: | 18 |
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