The Isometric Extension of an Into Mapping from the Unit Sphere $$ S{\left( {{\ell }^{\infty }_{{{\left( 2 \right)}}} } \right)} $$ to $$ S{\left( {L^{1} {\left( \mu \right)}} \right)} $$

2006 ◽  
Vol 22 (6) ◽  
pp. 1721-1724 ◽  
Author(s):  
Guang Gui Ding
Keyword(s):  
Unit Sphere ◽  
Isometric Extension

The problem of isometric extension in the unit sphere of the space

2011 ◽  
Vol 74 (3) ◽  
pp. 733-738 ◽  
Author(s):  
Xiaohong Fu ◽  
Stevo Stević
Keyword(s):  
Unit Sphere ◽  
Isometric Extension

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.

On the isometric extension problem

2013 ◽  
Vol 36 (3) ◽  
pp. 321-330
Author(s):  
Ruidong Wang
Keyword(s):  
Extension Problem ◽  
Isometric Extension
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