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

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.

UDC: 517.982.22

Received: 30.08.2022
Revised: 05.10.2022
Accepted: 14.11.2022

DOI: 10.18287/2541-7525-2022-28-1-2-23-31