Related papers: Strong subdifferentiability and local Bishop-Phelp…
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…
We prove that the class of positive operators from $L_\infty (\mu)$ to $Y$ has the Bishop-Phelps-Bollob\'as property for any positive measure $\mu$, whenever $Y$ is a uniformly monotone Banach lattice with a weak unit. The same result also…
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…
We show that the space of bounded and linear operators between spaces of continuous functions on compact Hausdorff topological spaces has the Bishop-Phelps-Bollob\'as property. A similar result is also proved for the class of compact…
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…
We study the Bishop-Phelps-Bollob\'as property for numerical radius (in short, BPBp-nu) and find sufficient conditions for Banach spaces ensuring the BPBp-nu. Among other results, we show that $L_1(\mu)$-spaces have this property for every…
We prove that the class of positive operators from $L_\infty (\mu)$ to $L_1 (\nu)$ has the Bishop-Phelps-Bollob\'as property for any positive measures $\mu$ and $\nu$. The same result also holds for the pair $(c_0, \ell_1)$. We also provide…
We introduce the so-called Bishop-Phelps-Bollob\'as property for positive functionals, a particular case of the Bishop-Phelps-Bollob\'as property for positive operators. First we show a version of the Bishop-Phelps-Bollob\'as theorem for…
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…
Extending the celebrated result by Bishop and Phelps that the set of norm attaining functionals is always dense in the topological dual of a Banach space, Bollob\'as proved the nowadays known as the Bishop-Phelps-Bollob\'as theorem, which…
The main purpose of this paper is to study the Bishop-Phelps-Bollob\'as property for operators on $c_0$-sum of euclidean spaces. We show that the pair $ (c_0\left(\bigoplus^{\infty}_{k=1}\ell^{k}_{2} \right),Y)$ has the…
We study the set $\operatorname{MA}(X,Y)$ of operators between Banach spaces $X$ and $Y$ that attain their minimum norm, and the set $\operatorname{QMA}(X,Y)$ of operators that quasi attain their minimum norm. We characterize the…
In this paper we study a weaker form of the property $\text{\textbf{L}}_{o,o}$ called the weak $\text{\textbf{L}}_{o,o}$ and its uniform version called the weak $\text{BPB}_{\text{op}}$ which is again a weaker form the property…
We study different aspects of the connections between local theory of Banach spaces and the problem of the extension of bilinear forms from subspaces of Banach spaces. Among other results, we prove that if $X$ is not a Hilbert space then…
We study Bollob\'as-type theorems for range strongly exposing operators. When such a theorem holds for operators from a Banach space $X$ into another Banach space $Y$, we say that the pair $(X,Y)$ satisfies the Bishop-Phelps-Bollob\'as…
This paper deals with the \emph{Bishop-Phelps-Bollob\'as property} (\emph{BPBp} for short) on bounded closed convex subsets of a Banach space $X$, not just on its closed unit ball $B_X$. We firstly prove that the \emph{BPBp} holds for…
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…
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 analyze some results for the sets of Lipschitz maps satisfying…
In this work we provide a characterization of distinct type of (linear and non-linear) maps between Banach spaces in terms of the differentiability of certain class of Lipschitz functions. Our results are stated in an abstract bornological…
Given two real Banach spaces $X$ and $Y$ with dimensions greater than one, it is shown that there is a sequence $\{T_n\}_{n\in \mathbb{N}}$ of norm attaining norm-one operators from $X$ to $Y$ and a point $x_0\in X$ with $\|x_0\|=1$, such…