10 citations · 22 across the 18 of their papers we have counts for
18 papers
A bi-Lipschitz characterization of strong minimum-attainment for Lipschitz maps
Geunsu Choi
We completely characterize the denseness of strongly minimum-attaining Lipschitz functions, a minimum analogue for strongly norm-attaining Lipschitz functions, in terms of bi-Lipsc…
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 Río, 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 n…
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…
Embeddings of infinite-dimensional spaces in the sets of norm-attaining Lipschitz functions
Geunsu Choi, Mingu Jung, Han Ju Lee +1
Motivated by the result of Dantas et. al. (2023) that there exist metric spaces for which the set of strongly norm-attaining Lipschitz functions does not contain an isometric copy…
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 and…
Weak-star quasi norm attaining operators
Geunsu Choi, Mingu Jung, Sun Kwang Kim +1
For Banach spaces and , a bounded linear operator is said to weak-star quasi attain its norm if the -closure of the image by of…
On a set of norm attaining operators and the strong Birkhoff-James orthogonality
Geunsu Choi, Mingu Jung, Sun Kwang Kim
Continuing the study of recent results on the Birkhoff-James orthogonality and the norm attainment of operators, we introduce a property namely the adjusted Bhatia-Šemrl property f…
A generalized ACK structure and the denseness of norm attaining operators
Geunsu Choi, Mingu Jung
Inspired by the recent work of Cascales et al., we introduce a generalized concept of ACK structure on Banach spaces. Using this property, which we call by the quasi-ACK structure,…
Norm attaining Lipschitz maps toward vectors
Geunsu Choi
We extend the recent result of G. Godefroy which concerns the existence of non-norm attaining Lipschitz maps in order to characterize the norm attainment toward vectors for Lipschi…
On the Crawford number attaining operators
Geunsu Choi, Han Ju Lee
We study the denseness of Crawford number attaining operators on Banach spaces. Mainly, we prove that if a Banach space has the RNP, then the set of Crawford number attaining opera…
On the Lipschitz numerical index of Banach spaces
Geunsu Choi, Mingu Jung, Hyung-Joon Tag
We provide some new consequences on the Lipschitz numerical radius and index which were introduced recently. More precisely, we give some renorming results on the Lipschitz numeric…
The Lipschitz bounded approximation property for operator ideals
Geunsu Choi, Mingu Jung
In this article, we introduce the Lipschitz bounded approximation property for operator ideals. With this notion, we extend the original work done by Godefroy and Kalton and give s…
The Birkhoff-James orthogonality and norm attainment for multilinear maps
Geunsu Choi, Sun Kwang Kim
Very recently, motivated by the result of Bhatia and Šemrl which characterizes the Birkhoff-James orthogonality of operators on a finite dimensional Hilbert space in terms of norm…
The Bishop-Phelps-Bollobás property on the space of -sum
Geunsu Choi, Sun Kwang Kim
The main purpose of this paper is to study Bishop-Phelps-Bollobás type properties on sum of Banach spaces. Among other results, we show that the pair has the Bis…
On quasi norm attaining operators between Banach spaces
Geunsu Choi, Yun Sung Choi, Mingu Jung +1
We introduce a weakened notion of norm attainment for bounded linear operators between Banach spaces which we call \emph{quasi norm attaining operators}. An operator $T\colon X \lo…
Emerging notions of norm attainment for Lipschitz maps between Banach spaces
Geunsu Choi, Yun Sung Choi, Miguel Martin
We classify several notions of norm attaining Lipschitz maps which were introduced previously, and present the relations among them in order to verify proper inclusions. We also an…