Results 71 to 80 of about 4,123 (102)

Injectivity in Banach spaces and the Mazur-Ulam theorem on isometries

, 1982
J. Gevirtz
semanticscholar   +1 more source

The Mazur-Ulam property for a Banach space which satisfies a separation condition (Research on preserver problems on Banach algebras and related topics)

The Mazur-Ulam property for a Banach space which satisfies a separation condition (Research on preserver problems on Banach algebras and related topics)
After some preparations in section 1, we recall the three well known concepts: the Choquet boundary, the Šilov boundary, and the strong boundary points in section 2. We need to define them by avoiding the confusion which appears because of the variety of names of these concepts; they sometimes differs from authors to authors.
openaire  

ISOMETRY ON LINEAR n-NORMED SPACES

, 2014
Yumei Ma
semanticscholar   +1 more source

The Mazur–Ulam property in ℓ∞-sum and c0-sum of strictly convex Banach spaces

Bulletin of the Australian Mathematical Society, 2020
In this article, we study the Mazur–Ulam property of the sum of two strictly convex Banach spaces. We give an equivalent form of the isometric extension problem and two equivalent conditions to decide whether all strictly convex Banach spaces admit the Mazur–Ulam property. We also find necessary and sufficient conditions under which the $\ell ^{1}$-sum
Julio Becerra Guerrero
semanticscholar   +6 more sources

Mankiewicz’s theorem and the Mazur–Ulam property for $\mathbf {C}^*$-algebras

Studia Mathematica, 2019
Michiya Mori, Narutaka Ozawa
semanticscholar   +3 more sources

The Mazur–Ulam property on Banach spaces of vector-valued continuous functions

, 2021
Julio Becerra Guerrero
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Tingley’s problem for complex Banach spaces which do not satisfy the Hausdorff distance condition

Banach Journal of Mathematical Analysis, 2022
In 2022, Hatori gave a sufficient condition for complex Banach spaces to have the complex Mazur–Ulam property. In this paper, we introduce a class of complex Banach spaces B that do not satisfy the condition but enjoy the property that every surjective ...
D. Cabezas, María Cueto-Avellaneda, Yuta Enami, T. Miura, A. M. Peralta   +4 more
semanticscholar   +1 more source

A set-valued extension of the Mazur–Ulam theorem

Studia Mathematica, 2021
. The Mazur–Ulam theorem states that every surjective isometry from a Banach space X to a Banach space Y is necessarily affine. Let K ( X ) (resp. K ( Y ) ) be the cone of all compact convex subsets of X (resp. Y ) endowed with the Hausdorff metric.
Lixin Cheng, Zheming Zheng
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Extending surjective isometries defined on the unit sphere of $$\ell _\infty (\Gamma )$$ℓ∞(Γ)

Revista Matemática Complutense, 2017
Let $$\Gamma $$Γ be an infinite set equipped with the discrete topology. We prove that the space $$\ell _{\infty }(\Gamma ,{\mathbb {C}}),$$ℓ∞(Γ,C), of all complex-valued bounded functions on $$\Gamma $$Γ, satisfies the Mazur–Ulam property, that is ...
A. M. Peralta
semanticscholar   +1 more source

ON THE EXTENSION OF ISOMETRIES BETWEEN THE UNIT SPHERES OF A $\text{JBW}^{\ast }$ -TRIPLE AND A BANACH SPACE

Journal of the Institute of Mathematics of Jussieu, 2018
We prove that if $M$ is a $\text{JBW}^{\ast }$ -triple and not a Cartan factor of rank two, then $M$ satisfies the Mazur–Ulam property, that is, every surjective isometry from the unit sphere of $M$ onto the unit sphere of another real Banach space $Y ...
J. Becerra-Guerrero, María Cueto-Avellaneda, Francisco J. Fern'andez-Polo, A. M. Peralta   +3 more
semanticscholar   +1 more source