0575754 - MÚ 2024 RIV US eng J - Journal Article
Maślany, Natalia
Isometries of combinatorial Tsirelson spaces.
Proceedings of the American Mathematical Society. Roč. 151, č. 10 (2023), s. 4475-4484. ISSN 0002-9939. E-ISSN 1088-6826
R&D Projects: GA ČR(CZ) GF20-22230L
Institutional support: RVO:67985840
Keywords : combinatorial spaces * combinatorial Tsirelson spaces * higher-order Schreier families
OECD category: Pure mathematics
Impact factor: 0.8, year: 2023 ; AIS: 0.719, rok: 2023
Method of publishing: Limited access
Result website:
https://doi.org/10.1090/proc/16465DOI: https://doi.org/10.1090/proc/16465

We extend existing results that characterize isometries on the Tsirelson-type spaces ... to the class ..., where S_\alpha denote the Schreier families of order \alpha. We prove that every isometry on ... is determined by a permutation of the first ... elements of the canonical unit basis followed by a possible sign-change of the corresponding coordinates together with a sign-change of the remaining coordinates. Moreover, we show that for the spaces ..., the isometries exhibit a more rigid character, namely, they are all implemented by a sign-change operation of the vector cordinates.
Permanent Link: https://hdl.handle.net/11104/0345484