On isometries and Tingley’s problem for the spaces T[θ,Sα], 1⩽α<ω1
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F23%3A00574194" target="_blank" >RIV/67985840:_____/23:00574194 - isvavai.cz</a>
Result on the web
<a href="https://dx.doi.org/10.4064/sm230505-4-9" target="_blank" >https://dx.doi.org/10.4064/sm230505-4-9</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4064/sm230505-4-9" target="_blank" >10.4064/sm230505-4-9</a>
Alternative languages
Result language
angličtina
Original language name
On isometries and Tingley’s problem for the spaces T[θ,Sα], 1⩽α<ω1
Original language description
We extend the existing results on surjective isometries of unit spheres in the Tsirelson space T[1/2,S1] to the class T[θ,Sα] for any integer θ─1≥2 and 1⩽α<ω1, where Sα denotes the Schreier family of order α. This positively answers Tingley’s problem for these spaces, which asks whether every surjective isometry between unit spheres can be extended to a surjective linear isometry of the entire space.nFurthermore, we improve the result stating that every linear isometry on T[θ,S1] (θ∈(0,1/2]) is determined by a permutation of the first ⌈θ─1⌉ elements of the canonical unit basis, followed by a possible sign change of the corresponding coordinates and a sign change of the remaining coordinates. Specifically, we prove that only the first ⌊θ─1⌋ elements can be permuted. This enables us to establish a sufficient condition for being a linear isometry in these spaces.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GF20-22230L" target="_blank" >GF20-22230L: Banach spaces of continuous and Lipschitz functions</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Studia mathematica
ISSN
0039-3223
e-ISSN
1730-6337
Volume of the periodical
273
Issue of the periodical within the volume
3
Country of publishing house
PL - POLAND
Number of pages
15
Pages from-to
285-299
UT code for WoS article
001110612100001
EID of the result in the Scopus database
2-s2.0-85180337821