Search
Search Results
-
On quasi norm attaining operators between Banach spaces
We provide a characterization of the Radon–Nikodým property for a Banach space Y in terms of the denseness of bounded linear operators into Y which...
-
-
Norm-attaining operators, variational principles, and Asplund spaces
In this chapter we shall review some results on extreme points, points of differentiability, farthest points and norm-attaining operators. All those...
-
Lipschitz (q, p)-Summing Maps from C(K)-Spaces to Metric Spaces
Variants of the notion of ( q , p )-summing operator are introduced in the setting of Lipschitz map**s acting between metric spaces. Some classes of...
-
Modulus support functionals, Rajchman measures and peak functions
In 2000 Victor Lomonosov suggested a counterexample to the complex version of the Bishop–Phelps theorem on modulus support functionals. We discuss...
-
Several Remarks on Norm Attainment in Tensor Product Spaces
The aim of this note is to obtain results about when the norm of a projective tensor product is strongly subdifferentiable. We prove that if
... -
Group invariant variational principles
In this paper we introduce a group invariant version of the well-known Ekeland variational principle. To achieve this, we define the concept of...
-
Simulation of the drawdown and its duration in Lévy models via stick-breaking Gaussian approximation
We develop a computational method for expected functionals of the drawdown and its duration in exponential Lévy models. It is based on a novel...
-
Miscellaneous applications
The following results are very important for understanding the relation of linear and metric structures of Banach spaces.
-
The Bishop–Phelps–Bollobás Theorem: An Overview
In this survey, we provide an overview from 2008 to 2021 about the Bishop–Phelps–Bollobás theorem.
-
Further miscellaneous applications
The one-sided directional derivatives were introduced by equations (4.5) and (4.6). Dini derivatives were used for dealing with continuous...
-
On the weak maximizing properties
Quite recently, a new property related to norm-attaining operators has been introduced: the weak maximizing property (WMP). In this note, we define a...
-
Open questions spread along the book and some additional ones
We gather in this chapter a list of open questions. The ones already mentioned along the text start with the reference to its location. Those...
-
Old and new challenges in Hadamard spaces
Hadamard spaces have traditionally played important roles in geometry and geometric group theory. More recently, they have additionally turned out to...
-
Linear Operators and Functionals
In this chapter we discuss one of the central concepts of functional analysis — linear operators. We first establish the three most important results...
-
Optimal learning
This paper studies the problem of learning an unknown function f from given data about f . The learning problem is to give an approximation
... 
-
Banach Spaces of Lipschitz Functions
In this chapter we introduce several Banach spaces of Lipschitz functions (Lipschitz functions vanishing at a fixed point, bounded Lipschitz...
-
Regularisation Functionals
Although some requirements concerning the families of regularisation functionals (Rα)α were needed in the theory of Part II, we did not yet address...