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Every commutative JB$$^*$$-triple satisfies the complex Mazur–Ulam property [PDF]
Annals of Functional Analysis, 2022 AbstractWe prove that every commutative JB$$^*$$∗-triple, represented as a space of continuous functions$$C_0^{\mathbb {T}}(L),$$C0T(L),satisfies the complex Mazur–Ulam property, that is, every surjective isometry from the unit sphere of$$C_0^{\mathbb {T}}(L)$$C0T(L)onto the unit sphere of any complex Banach space admits an extension to a surjective ...
David Cabezas +4 more
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Every non-smooth 2-dimensional Banach space has the Mazur–Ulam property [PDF]
Linear Algebra and its Applications, 2021 A Banach space $X$ has the $Mazur$-$Ulam$ $property$ if any isometry from the unit sphere of $X$ onto the unit sphere of any other Banach space $Y$ extends to a linear isometry of the Banach spaces $X,Y$. A Banach space $X$ is called $smooth$ if the unit ball has a unique supporting functional at each point of the unit sphere.
Тарас Банах +1 more
semanticscholar +7 more sources
Every 2-dimensional Banach space has the Mazur–Ulam property [PDF]
Linear Algebra and its Applications, 2021 8 ...
Тарас Банах
semanticscholar +4 more sources
The Mazur-Ulam property for commutative von Neumann algebras [PDF]
Linear and Multilinear Algebra, 2018 Let (Ω,μ) be a σ-finite measure space. Given a Banach space X, let the symbol S(X) stand for the unit sphere of X.
Antonio M. Peralta +1 more
semanticscholar +8 more sources
The Mazur–Ulam property for abelian $C^*$-algebras [PDF]
Studia Mathematica, 2022 The famous Mazur-Ulam theorem states that every surjective isometric mapping of a real normed space \(E\) to a real normed space \(F\) is affine. In a normed linear space, many properties of the space are determined by the action on the unit sphere of the space. Motivated by this, \textit{D.~Tingley} [Geom. Dedicata 22, 371--378 (1987; Zbl 0615.51005)]
Ruidong Wang, Yuexing Niu
semanticscholar +3 more sources
The Mazur–Ulam property for uniform algebras [PDF]
Studia Mathematica, 2022 We give a sufficient condition for a Banach space with which the homogeneous extension of a surjective isometry from the unit sphere of it onto another one is real-linear. The condition is satisfied by a uniform algebra and a certain extremely $C$-regular space of real-valued continuous functions.
Osamu Hatori
semanticscholar +4 more sources
The Mazur–Ulam property for the space of complex null sequences [PDF]
Linear and Multilinear Algebra, 2018 Given an infinite set Γ , we prove that the space of complex null sequences, c0(Γ) , satisfies the Mazur–Ulam property, that is, for each Banach space X, every surjective isometry from the unit sph...
A. Jiménez-Vargas +3 more
semanticscholar +6 more sources
The Mazur–Ulam property for two-dimensional somewhere-flat spaces
Linear Algebra and its Applications, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ruidong Wang, Xujian Huang
semanticscholar +3 more sources
On the Mazur--Ulam property for the space of Hilbert-space-valued\n continuous functions [PDF]
Journal of Mathematical Analysis and Applications, 2019 Let $K$ be a compact Hausdorff space and let $H$ be a real or complex Hilbert space with dim$(H_\mathbb{R})\geq 2$. We prove that the space $C(K,H)$ of all $H$-valued continuous functions on $K$, equipped with the supremum norm, satisfies the Mazur--Ulam property, that is, if $Y$ is any real Banach space, every surjective isometry $ $ from the unit ...
María Cueto-Avellaneda +1 more
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The Mazur-Ulam property for a Banach space which satisfies a separation condition [PDF]
, 2022 We study $C$-rich spaces, lush spaces, and $C$-extremely regular spaces concerning with the Mazur-Ulam property. We show that a uniform algebra and the real part of a uniform algebra with the supremum norm are $C$-rich spaces, hence lush spaces. We prove that a uniformly closed subalgebra of the algebra of complex-valued continuous functions on a ...
Osamu Hatori
openalex +3 more sources