On isometries and Tingley’s problem for the spaces $T[\theta , \mathcal{S}_{\alpha }]$, $1 \leqslant\alpha \lt \omega _{1}$

DOI10.4064/sm230505-4-9arXiv2305.01792MaRDI QIDQ6180245

Publication date: 19 January 2024

Published in: Studia Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2305.01792

zbMATH Keywords

isometry group Tingley's problem regular families Schreier families combinatorial spaces combinatorial Tsirelson spaces higher-order Schreier families

Mathematics Subject Classification ID

Classical Banach spaces in the general theory (46B25) Banach sequence spaces (46B45) Isometric theory of Banach spaces (46B04)

Cites Work

Unnamed Item
Unnamed Item
The isometric extension problem in the unit spheres of $l^p(\Gamma)(p>1)$ type spaces
On extension of isometries between unit spheres of $L_{p}(\mu )$ and $L_{p}(\nu ,H)$ ($1< p \neq 2$, $H$ is a Hilbert space)
Extension of isometries between the unit spheres of normed space $E$ and $C(\Omega)$
On extension of isometries and approximate isometries between unit spheres
The isometric extension of ``into mappings on unit spheres of $AL$-spaces
On isometric extension problem between two unit spheres
Not every Banach space contains an imbedding of $l_p$ or $c_0$
Extension of isometries on the unit sphere of $L^p$ spaces
Ramsey methods in analysis
Isometries of the unit sphere
Surjective isometries on Banach sequence spaces: a survey
Every $2$-dimensional Banach space has the Mazur-Ulam property
On extension of isometries between unit spheres of $\mathcal L^{\infty}(\Gamma)$-type space and a Banach space $E$
The isometric extension of the into mapping from a $\mathcal{L}^{\infty}(\Gamma)$-type space to some Banach space
The representation theorem of onto isometric mappings between two unit spheres of $l^\infty$-type spaces and the application on isometric extension problem
The 1-Lipschitz mapping between the unit spheres of two Hilbert spaces can be extended to a real linear isometry of the whole space
The representation theorem of onto isometric mappings between two unit spheres of $l^1(\Gamma)$ type spaces and the application to the isometric extension problem
Concerning the Szlenk index
A survey on Tingley’s problem for operator algebras
On extension of isometries between unit spheres of 𝐴𝐿_{𝑝}-spaces (0<𝑝<∞)
On the Extension Problems of Isometric and Nonexpansive Mappings
NONEXPANSIVE MAPPINGS ON THE UNIT SPHERES OF SOME BANACH SPACES
Isometries of combinatorial Tsirelson spaces

This page was built for publication: On isometries and Tingley’s problem for the spaces $T[\theta , \mathcal{S}_{\alpha }]$, $1 \leqslant\alpha \lt \omega _{1}$