Results 31 to 40 of about 4,123 (102)
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 +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 +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 +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
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 +2 more
wiley +1 more source
Mazur-Ulam type theorems for fuzzy normed spaces [PDF]
, 2017 In this paper, we provide Mazur-Ulam type results for (not necessarily surjective) maps preserving equality of fuzzy distance defined between two fuzzy normed spaces. Our main goal is to study the additivity of such generalizations of fuzzy isometries.
Font, Juan J. +3 more
core +2 more sources
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 +2 more
wiley +1 more source
The endpoint multilinear Kakeya theorem via the Borsuk--Ulam theorem [PDF]
, 2012 We give an essentially self-contained proof of Guth's recent endpoint multilinear Kakeya theorem which avoids the use of somewhat sophisticated algebraic topology, and which instead appeals to the Borsuk-Ulam ...
Anthony Carbery +12 more
core +2 more sources