Maps on Grassmann spaces preserving the minimal principal angle

Šemrl, Peter (author)

Let $n$ be a positive integer and $H$ a Hilbert space. The description of the general form of bijective maps on the set of $n$-dimensional subspaces of $H$ preserving the maximal principal angle has been obtained recently. This is a generalization of Wigner’s unitary-antiunitary theorem. In this paper we will obtain another extension of Wigner’s theorem in which the maximal principal angle is replaced by the minimal one. Moreover, in this case we do not need the bijectivity assumption.

• Language: English
• Keywords: Grassmann space, Hilbert space, orthogonal projection, principal angles
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2024
• Number of pages: Str. 109–122
• Numbering: Vol. 90, iss. 1/2
• PID: 20.500.12556/RUL-156055
• UDC: 517.9
• ISSN on article: 0001-6969
• DOI: 10.1007/s44146-023-00093-8
• COBISS.SI-ID: 189049859
• Publication date in RUL: 06.05.2024

Record is a part of a journal

• Title: Acta scientiarum mathematicarum
• Shortened title: Acta sci. math.
• Publisher: Springer Nature, Birkhäuser, University of Szeged
• ISSN: 0001-6969
• COBISS.SI-ID: 24863232

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.

Projects

• Funder: ARRS - Slovenian Research Agency
• Project number: J1-2454
• Name: Izomorfizmi, izometrije in ohranjevalci

• Funder: ARRS - Slovenian Research Agency
• Project number: P1-0288
• Name: Algebra in njena uporaba