Email this article Characterizations of geometric tripotents in strongly facially symmetric spaces
- Authors: Seypullaev J.K.1,2, Eshniyazova D.A.1, Dilmuratov D.D.1
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Affiliations:
- Karakalpak State University named after Berdakh
- V. I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences
- Issue: Vol 30, No 150 (2025)
- Pages: 160-169
- Section: Original articles
- URL: https://ogarev-online.ru/2686-9667/article/view/298090
- ID: 298090
Cite item
Abstract
The concept of a geometric tripotent is one of the key concepts in the theory of strongly facially symmetric spaces. This paper studies the properties of geometric tripotents. We establish necessary and sufficient conditions under which a norm-one element of the dual space (real or complex) of a strongly facially symmetric space is a geometric tripotent. We prove that two geometric tripotents in such a space are mutually orthogonal if and only if both their sum and difference have norm one. Furthermore, we show that the set of extreme points of the unit ball coincides with the set of maximal geometric tripotents in the dual of a strongly facially symmetric space. Finally, we examine the relationship between M-orthogonality and ordinary orthogonality in the dual of a complex strongly facially symmetric space, providing a geometric characterization of geometric tripotents.
About the authors
Jumabek Kh. Seypullaev
Karakalpak State University named after Berdakh; V. I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences
Author for correspondence.
Email: jumabek81@mail.ru
ORCID iD: 0000-0003-2938-2199
Doctor of Physical and Mathematical Science, Professor of Algebra and Functional Analysis Department; Leading Researcher
Uzbekistan, 1 Ch. Abdirov St., Nukus 230112, Uzbekistan; 9 University St., Tashkent 100174, UzbekistanDilfuza A. Eshniyazova
Karakalpak State University named after Berdakh
Email: dilfuz.4152@gmail.com
ORCID iD: 0009-0003-2291-0304
Assistant Professor of Algebra and Functional Analysis Department
Uzbekistan, 1 Ch. Abdirov St., Nukus 230112, UzbekistanDamir D. Dilmuratov
Karakalpak State University named after Berdakh
Email: dilmuratovdamir@gmail.com
Student, Mathematics Faculty
Uzbekistan, 1 Ch. Abdirov St., Nukus 230112, UzbekistanReferences
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