Extension of isometries on the unit sphere of L p spaces

2011 ◽  
Vol 28 (6) ◽  
pp. 1197-1208 ◽  
Author(s):  
Dong Ni Tan
Keyword(s):  
Unit Sphere ◽  
Extension Of Isometries

ON THE EXTENSION OF ISOMETRIES BETWEEN THE UNIT SPHERES OF A -TRIPLE AND A BANACH SPACE

2019 ◽  
pp. 1-27 ◽  
Author(s):  
Julio Becerra-Guerrero ◽  
María Cueto-Avellaneda ◽  
Francisco J. Fernández-Polo ◽  
Antonio M. Peralta
Keyword(s):  
Banach Space ◽  
Unit Sphere ◽  
Real Banach Space ◽  
Linear Isometry ◽  
Surjective Isometry ◽  
Extension Of Isometries ◽  
Real Linear ◽  
Cartan Factor

We prove that if $M$ is a $\text{JBW}^{\ast }$ -triple and not a Cartan factor of rank two, then $M$ satisfies the Mazur–Ulam property, that is, every surjective isometry from the unit sphere of $M$ onto the unit sphere of another real Banach space $Y$ extends to a surjective real linear isometry from $M$ onto $Y$ .

Extension of isometries on the unit sphere of l p (Γ) space

2010 ◽  
Vol 53 (4) ◽  
pp. 1085-1096 ◽  
Author(s):  
XiNian Fang ◽  
JianHua Wang
Keyword(s):  
Unit Sphere ◽  
Extension Of Isometries

scholarly journals Generalised Kochen–Specker Theorem in Three Dimensions

2021 ◽  
Vol 51 (3) ◽  
Author(s):  
Václav Voráček ◽  
Mirko Navara
Keyword(s):  
Unit Sphere ◽  
Hidden Variables ◽  
Three Dimensions ◽  
Quantum Theories

AbstractWe show that there is no non-constant assignment of zeros and ones to points of a unit sphere in $$\mathbb{R}^3$$ R 3 such that for every three pairwisely orthogonal vectors, an odd number of them is assigned 1. This is a new strengthening of the Bell–Kochen–Specker theorem, which proves the non-existence of hidden variables in quantum theories.

Vertex Subgroups of Irreducible Representations of Solvable Groups

1971 ◽  
Vol 23 (1) ◽  
pp. 12-21
Author(s):  
J. Malzan
Keyword(s):  
Vector Space ◽  
Unit Sphere ◽  
Convex Subset ◽  
Orthogonal Group ◽  
Solvable Groups ◽  
Fundamental Region ◽  
Irreducible Representations ◽  
Theoretical Problem ◽  
Real Vector ◽  
The Real

If ρ(G) is a finite, real, orthogonal group of matrices acting on the real vector space V, then there is defined [5], by the action of ρ(G), a convex subset of the unit sphere in V called a fundamental region. When the unit sphere is covered by the images under ρ(G) of a fundamental region, we obtain a semi-regular figure.The group-theoretical problem in this kind of geometry is to find when the fundamental region is unique. In this paper we examine the subgroups, ρ(H), of ρ(G) with a view of finding what subspace, W of V consists of vectors held fixed by all the matrices of ρ(H). Any such subspace lies between two copies of a fundamental region and so contributes to a boundary of both. If enough of these boundaries might be found, the fundamental region would be completely described.

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