Results 11 to 20 of about 631 (76)
MAZUR–ULAM PROPERTY OF THE SUM OF TWO STRICTLY CONVEX BANACH SPACES [PDF]
Bulletin of the Australian Mathematical Society, 2015 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
María Cueto-Avellaneda +1 more
+10 more sources
Geometric Invariants of Surjective Isometries between Unit Spheres
Mathematics, 2021 In this paper we provide new geometric invariants of surjective isometries between unit spheres of Banach spaces. Let X,Y be Banach spaces and let T:SX→SY be a surjective isometry.
Almudena Campos-Jiménez +1 more
doaj +1 more source
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.
María Cueto-Avellaneda +1 more
openaire +3 more sources
Every commutative JB$$^*$$-triple satisfies the complex Mazur–Ulam property
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
openaire +3 more sources
Generalized-lush spaces and the Mazur–Ulam property [PDF]
Studia Mathematica, 2013 We introduce a new class of Banach spaces, called generalized-lush spaces (GL-spaces for short), which contains almost-CL-spaces, separable lush spaces (specially, separable $C$-rich subspaces of $C(K)$), and even the two-dimensional space with hexagonal norm.
Tan, Dongni, Huang, Xujian, Liu, Rui
openaire +2 more sources
Every non-smooth 2-dimensional Banach space has the Mazur–Ulam property
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.
Taras Banakh, Javier Cabello Sánchez
openaire +3 more sources
The Mazur–Ulam property for uniform algebras
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.
openaire +2 more sources
Every 2-dimensional Banach space has the Mazur–Ulam property
Linear Algebra and its Applications, 2022 8 ...
openaire +2 more sources
On $n$-norm preservers and the Aleksandrov conservative $n$-distance problem [PDF]
, 2017 The goal of this paper is to point out that the results obtained in the recent papers [7,8,10,11] can be seriously strengthened in the sense that we can significantly relax the assumptions of the main results so that we still get the same conclusions. In
Gehér, Gy. P.
core +2 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...
Antonio Jiménez-Vargas +3 more
openaire +1 more source