Results 41 to 50 of about 631 (76)

An Approximate Version of the Jordan von Neumann Theorem for Finite Dimensional Real Normed Spaces [PDF]

, 2013
It is known that any normed vector space which satisfies the parallelogram law is actually an inner product space. For finite dimensional normed vector spaces over R, we formulate an approximate version of this theorem: if a space approximately satisfies
Passer, Benjamin
core   +1 more source

Isometries and approximate isometries

International Journal of Mathematics and Mathematical Sciences, Volume 25, Issue 2, Page 73-91, 2001., 2001
Some properties of isometric mappings as well as approximate isometries are studied.
Themistocles M. Rassias
wiley   +1 more source

Mankiewicz's theorem and the Mazur--Ulam property for C*-algebras

, 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.
Mori, Michiya, Ozawa, Narutaka
openaire   +2 more sources

The Mazur-Ulam property for a Banach space which satisfies a separation condition

, 2022
We study $C$-rich spaces, lush spaces, and $C$-extremely regular spaces concerning with the Mazur-Ulam property. We show that a uniform algebra and the real part of a uniform algebra with the supremum norm are $C$-rich spaces, hence lush spaces. We prove that a uniformly closed subalgebra of the algebra of complex-valued continuous functions on a ...
openaire   +2 more sources

The Mazur-Ulam property for the space of complex null sequences

, 2017
Given an infinite set $ $, we prove that the space of complex null sequences $c_0( )$ satisfies the Mazur-Ulam property, that is, for each Banach space $X$, every surjective isometry from the unit sphere of $c_0( )$ onto the unit sphere of $X$ admits a (unique) extension to a surjective real linear isometry from $c_0( )$ to $X$.
Jiménez-Vargas, Antonio, Campoy, Antonio Morales, Peralta, Antonio M., Ramírez, María Isabel   +3 more
openaire   +2 more sources

On the size of approximately convex sets in normed spaces

, 1999
Let X be a normed space. A subset A of X is approximately convex if $d(ta+(1-t)b,A) \le 1$ for all $a,b \in A$ and $t \in [0,1]$ where $d(x,A)$ is the distance of $x$ to $A$. Let $\Co(A)$ be the convex hull and $\diam(A)$ the diameter of $A$.
Dilworth, S. J., Howard, Ralph, Roberts, James W.   +2 more
core  

A strengthened Kadison’s transitivity theorem for unital JB$$^*$$-algebras with applications to the Mazur–Ulam property

Analysis and Mathematical Physics
Abstract 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
openaire   +1 more source

7th ESACP Congress in Caen April 1–5, 2001

, 2001
Analytical Cellular Pathology, Volume 22, Issue 1-2, Page 1-101, 2001.
wiley   +1 more source

Biomolecular Topology: Modelling and Analysis. [PDF]

Acta Math Sin Engl Ser, 2022
Liu J, Xia KL, Wu J, Yau SS, Wei GW.
europepmc   +1 more source

Refined stability of additive and quadratic functional equations in modular spaces. [PDF]

J Inequal Appl, 2017
Kim HM, Shin HY.
europepmc   +1 more source