Related papers: The Bishop-Phelps-Bollob\'as properties in complex…
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…
In this paper we introduce the strong Bishop-Phelps-Bollob\'as property (sBPBp) for bounded linear operators between two Banach spaces $X$ and $Y$. This property is motivated by a Kim-Lee result which states, under our notation, that a…
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…
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…
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…
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…
Given an open subset $U$ of a complex Banach space $E$, a weight $v$ on $U$ and a complex Banach space $F$, let $H^\infty_v(U,F)$ denote the Banach space of all weighted holomorphic mappings from $U$ into $F$, endowed with the weighted…
In a right quaternionic Hilbert space, following the complex formalism, decomposable operators, the so-called Bishop's property and the single valued extension property are defined and the connections between them are studied to certain…
We study uniform $\epsilon-$BPB approximations of bounded linear operators between Banach spaces from a geometric perspective. We show that for sufficiently small positive values of $\epsilon,$ many geometric properties like smoothness,…
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…
We show that the set of bounded linear operators from $X$ to $X$ admits a Bishop-Phelps-Bollob\'as type theorem for numerical radius whenever $X$ is $\ell_1(\mathbb{C})$ or $c_0(\mathbb{C})$. As an essential tool we provide two constructive…
We study the Bishop-Phelps-Bollob\'as property for operators from $\ell_\infty ^4 $ to a Banach space. For this reason we introduce an appropiate geometric property, namely the AHSp-$\ell_\infty ^4$. We prove that spaces $Y$satisfying…
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 study a Bishop-Phelps-Bollob\'as version of Lindenstrauss properties A and B. For domain spaces, we study Banach spaces $X$ such that $(X,Y)$ has the Bishop-Phelps-Bollob\'as property (BPBp) for every Banach space $Y$. We show that in…
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…
We introduce the notion of approximate norm attainment set of a bounded linear operator between Banach spaces and use it to obtain a complete characterization of smooth points in the space of compact linear operators, provided the domain…
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 $L_2$.
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 present a sufficient condition for a Banach space to have the approximate hyperplane series property (AHSP) which actually covers all known examples. We use this property to get a stability result to vector-valued spaces of integrable…
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…