Mingu Jung

On operators whose adjoints or second adjoints attain their norms

Sheldon Dantas, Mingu Jung, Miguel Martín

A long-standing open problem asks whether there exists an infinite-dimensional Banach space on which every bounded linear operator attains its norm. With $NA_{1} (X, Y)$ and $…

Optimal integral representations in projective tensor products: countability and topology

Mingu Jung

We study optimal integral representations in projective tensor products, focusing on two questions: whether they can always be replaced by countable optimal decompositions, and whe…

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…

Affine Approximation in Finite Nagata Dimension and Applications to Lipschitz-free spaces

Mingu Jung, Colin Petitjean, Antonín Prochazka +1

We show that if $M$ is a metric space of Nagata dimension at most $d$ , then there exists an atlas on $M$ modeled on $R^{d}$ such that every Lipschitz map $f : M \to Y$ (with val…

Integral representations of projective norm-attaining tensors

Ramón J. Aliaga, Sheldon Dantas, Juan Guerrero-Viu +2

We introduce a Bochner integral approach to projective norm attainment in tensor products of Banach spaces by defining the class of integral projective norm-attaining tensors. This…

math.FA2025

Group equivariant Radon-Nikodým property and its characterizations

Sheldon Dantas, Michal Doucha, Mingu Jung +1

We introduce and study equivariant versions of the Radon-Nikodým property for Banach spaces, together with the closely related notions such as dentability, the Bishop-Phelps and Kr…

math.FA2025

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…

math.FA2024

On the strongly subdifferentiable points in Lipschitz-free spaces

Christian Cobollo, Sheldon Dantas, Petr Hájek +1

In this paper, we present some sufficient conditions on a metric space $M$ for which every molecule is a strongly subdifferentiable (SSD, for short) point in the Lipschitz-free spa…

math.FA2024

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 $M$ , 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…

Linear structures in the set of non-norm-attaining operators on Banach spaces

Sheldon Dantas, Javier Falcó, Mingu Jung +1

We study large linear structures inside sets arising in the theory of norm-attaining operators. We provide several results in the context of lineability, spaceability, maximal-spac…

The Daugavet and Delta-constants of points in Banach spaces

Geunsu Choi, Mingu Jung

We introduce two new notions called the Daugavet constant and $Δ$ -constant of a point, which measure quantitatively how far the point is from being Daugavet point and $Δ$ -point and…

Rank-one perturbations and norm-attaining operators

Gonzalo Martínez-Cervantes, Mingu Jung, Abraham Rueda Zoca

The main goal of this article is to show that for every (reflexive) infinite-dimensional Banach space $X$ there exists a reflexive Banach space $Y$ and $T, R \in L (X, Y)$ …

A note on numerical radius attaining mappings

Mingu Jung

We prove that if every bounded linear operator (or $N$ -homogeneous polynomials) with the compact approximation property attains its numerical radius, then $X$ is a finite dimension…

Weak-star quasi norm attaining operators

Geunsu Choi, Mingu Jung, Sun Kwang Kim +1

For Banach spaces $X$ and $Y$ , a bounded linear operator $T : X ⟶ Y^{*}$ is said to weak-star quasi attain its norm if the $σ (Y^{*}, Y)$ -closure of the image by $T$ of…

On the strong subdifferentiability of the homogeneous polynomials and (symmetric) tensor products

Sheldon Dantas, Mingu Jung, Martin Mazzitelli +1

In this paper, we study the (uniform) strong subdifferentiability of the norms of the Banach spaces $P (^{N} X, Y^{*})$ , $X \otimes^_{π} \dots \otimes^_{π} X$ and $\hat{\…

math.FA2022★ 1 cited

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,…

math.FA2022★ 11 cited

Residuality in the set of norm attaining operators between Banach spaces

Mingu Jung, Miguel Martin, Abraham Rueda Zoca

We study the relationship between the residuality of the set of norm attaining functionals on a Banach space and the residuality and the denseness of the set of norm attaining oper…

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…

Boundaries for Gelfand transform images of Banach algebras of holomorphic functions

Yun Sung Choi, Mingu Jung

Let $A$ be a Banach algebra of bounded holomorphic functions on the open unit ball $B_{X}$ of a complex Banach space $X$ . Considering the Gelfand transform image $\widehat{…

Group invariant operators and some applications on norm-attaining theory

Sheldon Dantas, Javier Falcó, Mingu Jung

In this paper, we study geometric properties of the set of group invariant continuous linear operators between Banach spaces. In particular, we present group invariant versions of…

math.FA2021★ 1 cited

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…