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We study the stability behavior of the Bishop-Phelps-Bollob\'as property for Lipschitz maps (Lip-BPB property). This property is a Lipschitz version of the classical Bishop-Phelps-Bollob\'as property and deals with the possibility of…

Functional Analysis · Mathematics 2020-04-23 Rafael Chiclana , Miguel Martin

In this paper, we introduce the notion of the Bishop-Phelps-Bollob\'as property for numerical radius (BPBp-$\nu$) for a subclass of the space of bounded linear operators. Then, we show that certain subspaces of $\mathcal{L}(L_1(\mu))$ have…

Functional Analysis · Mathematics 2021-06-14 M. D. Acosta , M. Fakhar , M. Soleimani-Mourchehkhorti

The main purpose of this paper is to study Bishop-Phelps-Bollob\'as type properties on $c_0$ sum of Banach spaces. Among other results, we show that the pair $(c_0(X),Y)$ has the Bishop-Phelps-Bollob\'as property (in short, BPBp) for…

Functional Analysis · Mathematics 2022-02-23 Geunsu Choi , Sun Kwang Kim

In this paper we consider a stronger property than the Bishop-Phelps-Bollob\'{a}s property for various classes of operators on a complex Hilbert space. The Bishop-Phelps-Bollob\'as {\it point} property for some class $\mathcal{A} \subset…

Functional Analysis · Mathematics 2019-11-04 Yun Sung Choi , Sheldon Dantas , Mingu Jung

We prove that the class of Banach spaces $Y$ such that the pair $(\ell_1, Y)$ has the Bishop-Phelps-Bollob\'as property for operators is stable under finite products when the norm of the product is given by an absolute norm. We also provide…

Functional Analysis · Mathematics 2021-06-14 M. D. Acosta , M. Soleimani-Mourchehkhorti

The Bishop-Phelps-Bollob\'{a}s property deals with simultaneous approximation of an operator $T$ and a vector $x$ at which $T$ nearly attains its norm by an operator $T_0$ and a vector $x_0$, respectively, such that $T_0$ attains its norm…

Functional Analysis · Mathematics 2017-04-07 Bernardo Cascales , Antonio J. Guirao , Vladimir Kadets , Mariia Soloviova

Let $X$ be a complex Banach space. We prove that if $L$ is an extremally disconnected compact Hausdorff topological space, then the pair $(X, C(L))$ satisfies the Bishop-Phelps-Bollob\'as property (BPBp for short). As a byproduct, we obtain…

Functional Analysis · Mathematics 2024-03-08 Tirthankar Bhattacharyya , Mainak Bhowmik , Kousik Dhara

In this paper, we introduce and study a Lipschitz version of the Bishop-Phelps-Bollob\'as property (Lip-BPB property). This property deals with the possibility of making a uniformly simultaneous approximation of a Lipschitz map $F$ and a…

Functional Analysis · Mathematics 2019-06-18 Rafael Chiclana , Miguel Martin

It is shown that the Bishop-Phelps-Bollob\'as theorem holds for bilinear forms on the complex $C_0(L_1)\times C_0(L_2)$ for arbitrary locally compact topological Hausdorff spaces $L_1$ and $L_2$.

Functional Analysis · Mathematics 2017-04-25 Sun Kwang Kim , Han Ju Lee , Miguel Martin

We give a class of bounded closed sets $C$ in a Banach space satisfying a generalized and stronger form of the Bishop-Phelps property studied by Bourgain in \cite{Bj} for dentable sets. A version of the {\it ``Bishop-Phelps-Bollob\'as"}…

Functional Analysis · Mathematics 2025-07-22 Mohammed Bachir

We introduce two Bishop-Phelps-Bollob\'as moduli which measure, for a given Banach space, what is the best possible Bishop-Phelps-Bollob\'as theorem in this space. We show that there is a common upper bound for these moduli for all Banach…

Functional Analysis · Mathematics 2021-06-21 Mario Chica , Vladimir Kadets , Miguel Martin , Soledad Moreno , Fernando Rambla

We continue a line of study about some local versions of Bishop-Phelps-Bollob\'as type properties for bounded linear operators. We introduce and focus our attention on two of these local properties, which we call L$_{p, o}$ and L$_{o, p}$,…

Functional Analysis · Mathematics 2019-06-03 Sheldon Dantas , Sun Kwang Kim , Han Ju Lee , Martin Mazzitelli

It has been recently presented some local versions of the Bishop-Phelps-Bollob\'as type property for operators. In the present article, we continue studying these properties for multilinear mappings. We show some differences between the…

Functional Analysis · Mathematics 2019-05-22 Sheldon Dantas , Sun Kwang Kim , Han Ju Lee , Martin Mazzitelli

We show that the pair $(C(K),X)$ has the Bishop-Phelps-Bolloba\'as property for operators if $K$ is a compact Hausdorff space and $X$ is a uniformly convex space.

Functional Analysis · Mathematics 2014-07-31 Sun Kwang Kim , Han Ju Lee

In this paper we study conditions assuring that the Bishop-Phelps-Bollob\'as property (BPBp, for short) is inherited by absolute summands of the range space or of the domain space. Concretely, given a pair (X, Y) of Banach spaces having the…

Functional Analysis · Mathematics 2019-04-24 Yun Sung Choi , Sheldon Dantas , Mingu Jung , Miguel Martín

We consider linear operators defined on a subspace of a complex Banach space into its topological antidual acting positively in a natural sense. The goal of this paper is to investigate of this kind of operators. The main theorem is a…

Functional Analysis · Mathematics 2014-09-12 Zoltán Sebestyén , Zsolt Szűcs , Zsigmond Tarcsay

We study the Bishop-Phelps-Bollob\'as property for numerical radius restricted to the case of compact operators (BPBp-nu for compact operators in short). We show that $C_0(L)$ spaces have the BPBp-nu for compact operators for every…

Functional Analysis · Mathematics 2021-02-23 Domingo Garcia , Manuel Maestre , Miguel Martin , Oscar Roldan

We study the Bishop-Phelps-Bollob\'as property for operators between Banach spaces. Sufficient conditions are given for generalized direct sums of Banach spaces with respect to a~uniformly monotone Banach sequence lattice to have the…

Functional Analysis · Mathematics 2021-06-14 M. D. Acosta , M. Mastyło , M. Soleimani-Mourchehkhorti

We study approximation of operators between Banach spaces $X$ and $Y$ that nearly attain their norms in a given point by operators that attain their norms at the same point. When such approximations exist, we say that the pair $(X, Y)$ has…

Functional Analysis · Mathematics 2018-11-20 Sheldon Dantas , Vladimir Kadets , Sun Kwang Kim , Han Ju Lee , Miguel Martin

Let $\mathbb{D}$ represent the open unit disc in $\mathbb{C}$. Denote by $A(\mathbb{D})$ the disc algebra, and $\mathscr{B}(X, A(\mathbb{\mathbb{D}}))$ the Banach space of all bounded linear operators from a Banach space $X$ into…

Functional Analysis · Mathematics 2023-05-02 Neeru Bala , Jaydeb Sarkar , Aryaman Sensarma