Reflexivity of finite-dimensional sets of operators

Bračič, Janko (author)

A non-empty set of operators $\mathcal{M}$ is reflexive if an operator $T$ is in $\mathcal{M}$ if and only if $Tx\in \overline{\mathcal{M} x}$, for all vectors $x$. In this paper, we study the reflexivity of finite-dimensional sets of operators. We introduce the class of flat sets of operators and prove several results related to the reflexivity of these sets; in particular, we show that the convex hull of three (or fewer) operators is reflexive.

• Language: English
• Keywords: reflexive set of operators, locally linearly dependent operators, flat sets of operators
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: NTF - Faculty of Natural Sciences and Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2023
• Number of pages: 16 str.
• Numbering: Vol. 17, iss. 4, art. 72
• PID: 20.500.12556/RUL-152551
• UDC: 517.9
• ISSN on article: 1735-8787
• DOI: 10.1007/s43037-023-00299-6
• COBISS.SI-ID: 169806083
• Publication date in RUL: 27.11.2023

Record is a part of a journal

• Title: Banach journal of mathematical analysis
• Publisher: Springer Nature, Birkhäuser, Tusi Mathematical Research Group
• ISSN: 1735-8787
• COBISS.SI-ID: 14518617

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: refleksivna množica operatorjev, lokalno linearno odvisni operatorji, ploščate množice operatorjev

Projects

• Funder: ARRS - Slovenian Research Agency
• Project number: P2-0268
• Name: Geotehnologija