scholarly journals Sharp corner points and isometric extension problem in Banach spaces

2013 ◽  
Vol 405 (1) ◽  
pp. 297-309 ◽  
Author(s):  
Guang-Gui Ding ◽  
Jian-Ze Li
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 36 (3) ◽  
pp. 321-330
Author(s):  
Ruidong Wang

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.


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