A Property in Vector-Valued Function Spaces [PDF]
Results in Mathematics, 2021 This paper deals with a property which is equivalent to generalised-lushness for separable spaces. It thus may be seemed as a geometrical property of a Banach space which ensures the space to have the Mazur–Ulam property.
D. Tan, Kexin Zhao
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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
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Extension of isometries from the unit sphere of a rank-2 Cartan factor [PDF]
Analysis and Mathematical Physics, 2019 We prove that every surjective isometry from the unit sphere of a rank-2 Cartan factor C onto the unit sphere of a real Banach space Y , admits an extension to a surjective real linear isometry from C onto Y . The conclusion also covers the case in which
Ondvrej F. K. Kalenda, A. M. Peralta
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On the extension of surjective isometries whose domain is the unit sphere of a space of compact operators [PDF]
Filomat, 2020 We prove that every surjective isometry from the unit sphere of the space K(H), of all compact operators on an arbitrary complex Hilbert space H, onto the unit sphere of an arbitrary real Banach space Y can be extended to a surjective real linear ...
A. M. Peralta
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Corrigendum to “On the Mazur-Ulam theorem in non-Archimedean fuzzy anti-2-normed spaces” [PDF]
Filomat, 2021 In this note we correct a paper by D. Kang (?On the Mazur-Ulam theorem in non-Archimedean fuzzy anti-2-normed spaces?, Filomat, 2017). The research in that paper applies to what the author calls strictly convex spaces. Nevertheless, we prove that this
J. S'anchez, Jos'e Navarro Garmendia
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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.
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Borsuk–Ulam Property and Sectional Category [PDF]
Bulletin of the Iranian Mathematical Society, 2022 For a Hausdorff space X , a free involution $$\tau :X\rightarrow X$$ τ : X → X and a Hausdorff space Y , we discover a connection between the sectional category of the double covers $$q:X\rightarrow X/\tau $$ q : X → X / τ and $$q^Y:F(Y,2)\rightarrow D(Y,
C. A. I. Zapata, D. Gonçalves
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The Mazur-Ulam property for a Banach space which satisfies a separation condition (Research on preserver problems on Banach algebras and related topics) [PDF]
, 2023 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
HATORI, Osamu
core
A contribution to the Aleksandrov conservative distance problem in two dimensions [PDF]
, 2015 Let $E$ be a two-dimensional real normed space. In this paper we show that if the unit circle of $E$ does not contain any line segment such that the distance between its endpoints is greater than 1, then every transformation $\phi\colon E\to E$ which ...
Gehér, György Pál
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Extension of isometries and the Mazur–Ulam property
, 2020 María de Nazaret Cueto Avellaneda
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