Results 11 to 20 of about 565 (36)

Isometries of the unitary groups and Thompson isometries of the spaces of invertible positive elements in C*-algebras [PDF]

, 2014
We show that the existence of a surjective isometry (which is merely a distance preserving map) between the unitary groups of unital C*-algebras implies the existence of a Jordan *-isomorphism between the algebras.
Andruchow, Conway, Corach, Ellis, Fleming, Fleming, Hatori, Hatori, Hatori, Hatori, Hatori, Hu, Kadison, Kadison, Kadison, Kubo, Lajos Molnár, Mankiewicz, Miura, Molnár, Osamu Hatori, Sakai, Sakai, Sourour, Thompson, Šemrl   +25 more
core   +1 more source

Maps Preserving Schatten p‐Norms of Convex Combinations

Abstract and Applied Analysis, Volume 2014, Issue 1, 2014., 2014
We study maps ϕ of positive operators of the Schatten p‐classes (1 < p < +∞), which preserve the p‐norms of convex combinations, that is, ∥tρ+(1-t)σ∥p=∥tϕ(ρ)+(1-t)ϕ(σ)∥p, ∀ρ,σ∈𝒮p+(H)1, t ∈[0,1]. They are exactly those carrying the form ϕ(ρ) = UρU* for a unitary or antiunitary U. In the case p = 2, we have the same conclusion whenever it just holds ∥ρ+σ∥
David Li-Wei Kuo, Ming-Cheng Tsai, Ngai-Ching Wong, Jun Zhang, Antonio M. Peralta   +4 more
wiley   +1 more source

A Generalized Mazur‐Ulam Theorem for Fuzzy Normed Spaces

Abstract and Applied Analysis, Volume 2014, Issue 1, 2014., 2014
We introduce fuzzy norm-preserving maps, which generalize the concept of fuzzy isometry. Based on the ideas from Vogt, 1973, and Väisälä, 2003, we provide the following generalized version of the Mazur‐Ulam theorem in the fuzzy context: let X, Y be fuzzy normed spaces and let f : X → Y be a fuzzy norm‐preserving surjection satisfying f(0) = 0.
J. J. Font, J. Galindo, S. Macario, M. Sanchis, Salvador Romaguera   +4 more
wiley   +1 more source

On Isometric Extension in the Space sn(H)

Journal of Function Spaces, Volume 2014, Issue 1, 2014., 2014
We study the problem of isometric extension on a sphere of the space sn(H). We give an affirmative answer to Tingley’s problem in the space sn(H).
Xiaohong Fu, Naseer Shahzad
wiley   +1 more source

Nonlinear Isometries on Schatten‐p Class in Atomic Nest Algebras

Abstract and Applied Analysis, Volume 2014, Issue 1, 2014., 2014
Let H be a complex Hilbert space; denote by Alg 𝒩 and 𝒞p(H) the atomic nest algebra associated with the atomic nest 𝒩 on H and the space of Schatten‐p class operators on, H respectively. Let 𝒞p(H)∩Alg 𝒩 be the space of Schatten‐p class operators in Alg 𝒩.
Kan He, Qing Yuan, Feliz Minhós
wiley   +1 more source

Linear maps on the space of all bounded observables preserving maximal deviation [PDF]

, 2003
In this paper we determine all the bijective linear maps on the space of bounded observables which preserve a fixed moment or the variance. Nonlinear versions of the corresponding results are also presented.Comment: 27 pages. To appear in J.
Barczy, M., Molnar, L.
core   +3 more sources

On the Aleksandrov‐Rassias Problems on Linear n‐Normed Spaces

Journal of Function Spaces, Volume 2013, Issue 1, 2013., 2013
This paper generalizes T. M. Rassias′ results in 1993 to n‐normed spaces. If X and Y are two real n‐normed spaces and Y is n‐strictly convex, a surjective mapping f : X → Y preserving unit distance in both directions and preserving any integer distance is an n‐isometry.
Yumei Ma, Ji Gao
wiley   +1 more source

Linear Isometries between Real Banach Algebras of Continuous Complex‐Valued Functions

Journal of Operators, Volume 2013, Issue 1, 2013., 2013
Let X and Y be compact Hausdorff spaces, and let τ and η be topological involutions on X and Y, respectively. In 1991, Kulkarni and Arundhathi characterized linear isometries from a real uniform function algebra A on (X, τ) onto a real uniform function algebra B on (Y, η) applying their Choquet boundaries and showed that these mappings are weighted ...
Davood Alimohammadi, Hadis Pazandeh, Jan Lang   +2 more
wiley   +1 more source

Multiplicative Isometries on Some F‐Algebras of Holomorphic Functions

Journal of Function Spaces, Volume 2013, Issue 1, 2013., 2013
Multiplicative (but not necessarily linear) isometries of Mp(X) onto Mp(X) will be described, where Mp(X) (p ≥ 1) are F‐algebras included in the Smirnov class N∗(X).
Yasuo Iida, Kazuhiro Kasuga, Gestur Ólafsson   +2 more
wiley   +1 more source

On the Mazur‐Ulam Theorem in Non‐Archimedean Fuzzy n‐Normed Spaces

International Scholarly Research Notices, Volume 2013, Issue 1, 2013., 2013
The motivation of this paper is to present a new notion of non‐Archimedean fuzzy n‐normed space over a field with valuation. We obtain a Mazur‐Ulam theorem for fuzzy n‐isometry mappings in the strictly convex non‐Archimedean fuzzy n‐normed spaces. We also prove that the interior preserving mapping carries the barycenter of a triangle to the barycenter ...
Tian Zhou Xu, M. Tang, C. Zhu
wiley   +1 more source