A strengthened Kadison's transitivity theorem for unital JB$^*$-algebras with applications to the Mazur--Ulam property [PDF]
, 2023 The principal result in this note is a strengthened version of Kadison's transitivity theorem for unital JB$^*$-algebras, showing that for each minimal tripotent $e$ in the bidual, $\mathfrak{A}^{**}$, of a unital JB$^*$-algebra $\mathfrak{A}$, there exists a self-adjoint element $h$ in $\mathfrak{A}$ satisfying $e\leq \exp(ih)$, that is, $e$ is ...
Antonio M. Peralta, Radovan Švarc
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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.
Dongni Tan, Xujian Huang, Rui Liu
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Generalized-Lush Spaces and the Mazur-Ulam Property [PDF]
, 2012 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
Dongni Tan, Xujian Huang, Rui Liu
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The Mazur--Ulam property in $\ell_\infty$-sum and $c_0$-sum of strictly convex Banach spaces [PDF]
, 2019 In this paper we deal with those Banach spaces $Z$ which satisfy the Mazur--Ulam property, namely that every surjective isometry $ $ from the unit sphere of $Z$ to the unit sphere of any Banach space $Y$ admits an unique extension to a surjective real-linear isometry from $Z$ to $Y$.
Julio Becerra Guerrero
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A strengthened Kadison’s transitivity theorem for unital JB$$^*$$-algebras with applications to the Mazur–Ulam property [PDF]
Analysis and Mathematical PhysicsAbstract The principal result in this note is a strengthened version of Kadison’s transitivity theorem for unital JB $$^*$$ ∗ -algebras, showing that ...
Antonio M. Peralta, Radovan Švarc
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Mankiewicz's theorem and the Mazur--Ulam property for C*-algebras [PDF]
, 2018 We prove that every unital C*-algebra $A$ has the Mazur--Ulam property. Namely, every surjective isometry from the unit sphere $S_A$ of $A$ onto the unit sphere $S_Y$ of another normed space $Y$ extends to a real linear map. This extends the result of A. M. Peralta and F. J.
Michiya Mori, Narutaka Ozawa
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The core of the unit sphere of a Banach space
AIMS MathematicsA geometric invariant or preserver is essentially a geometric property of the unit sphere of a real Banach space that remains invariant under the action of a surjective isometry onto the unit sphere of another real Banach space. A new geometric invariant
Almudena Campos-Jiménez +1 more
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A note on the Mazur–Ulam property of almost-CL-spaces
Journal of Mathematical Analysis and Applications, 2013 We introduce the (T)-property, and prove that every Banach space with the (T)-property has the Mazur-Ulam property (briefly MUP). As its immediate applications, we obtain that almost-CL-spaces admitting a smooth point(specially, separable almost-CL-spaces) and a two-dimensional space whose unit sphere is a hexagon has the MUP.
Dongni Tan, Rui Liu
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MAZUR–ULAM PROPERTY OF THE SUM OF TWO STRICTLY CONVEX BANACH SPACES [PDF]
Bulletin of the Australian Mathematical Society, 2015 Jianze Li
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A Note on The Mazur-Ulam Property of Almost-CL-spaces [PDF]
, 2012 Dongni Tan, Rui Liu
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