On isometric extension problem between two unit spheres

2009 ◽  
Vol 52 (10) ◽  
pp. 2069-2083 ◽  
Author(s):  
GuangGui Ding
2013 ◽  
Vol 36 (3) ◽  
pp. 321-330
Author(s):  
Ruidong Wang

2015 ◽  
Vol 93 (3) ◽  
pp. 473-485 ◽  
Author(s):  
JIAN-ZE LI

In this article, we study the Mazur–Ulam property of the sum of two strictly convex Banach spaces. We give an equivalent form of the isometric extension problem and two equivalent conditions to decide whether all strictly convex Banach spaces admit the Mazur–Ulam property. We also find necessary and sufficient conditions under which the $\ell ^{1}$-sum and the $\ell ^{\infty }$-sum of two strictly convex Banach spaces admit the Mazur–Ulam property.


2013 ◽  
Vol 88 (3) ◽  
pp. 369-375 ◽  
Author(s):  
GUANG-GUI DING ◽  
JIAN-ZE LI

AbstractWe prove that any surjective isometry between unit spheres of the ${\ell }^{\infty } $-sum of strictly convex normed spaces can be extended to a linear isometry on the whole space, and we solve the isometric extension problem affirmatively in this case.


2016 ◽  
Vol 71 (3-4) ◽  
pp. 749-781 ◽  
Author(s):  
Norbert Hungerbühler ◽  
Micha Wasem

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