5 papers
On absolute strong exposure for Lipschitz maps
Geunsu Choi, Mingu Jung
We introduce strongly exposing Lipschitz maps, a vector-valued extension of Weaver's peaking functions and a nonlinear analogue of absolutely strongly exposing operators. Our main…
Range strongly exposing operators between Banach spaces
Geunsu Choi, Helena del RÃo, Audrey Fovelle +2
We introduce a new class of bounded linear operators, called range strongly exposing (RSE) operators, which form a natural intermediate class: weaker than Bourgain's absolutely str…
Approximations of Lipschitz maps with maximal derivatives on Banach spaces
Geunsu Choi
We study two types of approximations of Lipschitz maps with derivatives of maximal slopes on Banach spaces. First, we characterize the Radon-Nikodým property in terms of strongly…
The Daugavet and Delta-constants of points in Banach spaces
Geunsu Choi, Mingu Jung
We introduce two new notions called the Daugavet constant and -constant of a point, which measure quantitatively how far the point is from being Daugavet point and -point a…
Linear structures of norm-attaining Lipschitz functions and their complements
Geunsu Choi, Mingu Jung, Han Ju Lee +1
We solve two main questions on linear structures of (non-)norm-attaining Lipschitz functions. First, we show that for every infinite metric space , the set consisting of Lipschi…