Results 21 to 30 of about 3,395 (68)
Geometric Invariants of Surjective Isometries between Unit Spheres
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
Extension of isometries from the unit sphere of a rank-2 Cartan factor [PDF]
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
semanticscholar +2 more sources
On the extension of surjective isometries whose domain is the unit sphere of a space of compact operators [PDF]
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
semanticscholar +1 more source
Corrigendum to “On the Mazur-Ulam theorem in non-Archimedean fuzzy anti-2-normed spaces” [PDF]
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
semanticscholar +1 more source
Borsuk–Ulam Property and Sectional Category [PDF]
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
semanticscholar +1 more source
Extension of isometries and the Mazur–Ulam property
María de Nazaret Cueto Avellaneda
openaire +2 more sources
Some remarks on generalised lush spaces [PDF]
X. Huang et al. recently introduced the notion of generalised lush (GL) spaces, which, at least for separable spaces, is a generalisation of the concept of lushness introduced by K. Boyko et al. in 2007. The main result of Huang et al.
Jan-David Hardtke
semanticscholar +1 more source
Injectivity in Banach spaces and the Mazur-Ulam theorem on isometries
A mapping / of an open subset U of a Banach space X into another Banach space Y is said to be (m, M)-isometric if it is a local homeomorphism for which M > D + f(x) and m « D-f(x) for all x G U, where D+f(x) and D~f(x) are, respectively, the upper and ...
J. Gevirtz
semanticscholar +1 more source
On non-L0-linear perturbations of random isometries in random normed modules
The purpose of this paper is to study non-L0-linear perturbations of random isometries in random normed modules. Let (Ω,F,P) be a probability space, K the scalar field R of real numbers or C of complex numbers, L0(F,K) the equivalence classes of K-valued
Shien Zhao, Yuan-e Zhao, Ming-Jia Yao
semanticscholar +2 more sources
On maps which preserve equality of distance in F-spaces [PDF]
In order to generalize the results of Mazur-Ulam and Vogt, we shall prove that any map T which preserves equality of distance with T(0)=0 between two F-spaces without surjective condition is linear.
D. Tan
semanticscholar +1 more source