Search
Search Results
-
The pointwise James type constant
In 2008, Takahashi introduced the James type constants. We discuss here the pointwise James type constant: for all x ∈ X , ∥ x ∥ = 1, We show that in...
-
An Introduction to Matrix Convex Sets and Free Spectrahedra
The purpose of this paper is to give a self-contained overview of the theory of matrix convex sets and free spectrahedra. We will give new proofs and...
-
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...
-
Subdifferentiability and polyhedrality of the norm
Let X be an infinite dimensional real Banach space. In this paper, motivated by the work of Contreras et al. (J Math Anal Appl 198:227–236, 1996) we...
-
Sequential Analogues of the Lyapunov and Krein–Milman Theorems in Fréchet Spaces
In this paper we develop the theory of anti-compact sets we introduced earlier. We describe the class of Fréchet spaces where anti-compact sets...
-
Remarkable Consequences of Convexity
This chapter is devoted to remarkable topics of convex analysis that, together with subdifferential calculus, Fenchel conjugates and related results...
-
Glivenko–Cantelli classes and NIP formulas
We give several new equivalences of NIP for formulas and new proofs of known results using Talagrand (Ann Probab 15:837–870, 1987) and Haydon et al....
-
An Inequality for Polynomials on the Standard Simplex
Let \(\varDelta := \{ (x,y) \in \mathbb {R}^2: x \ge 0,~ y \ge 0,~ x+y \le 1 \} \)...
-
On the Heinz mean in multiple variables
The fundamental goal of the present paper is to investigate an extension of the so-called Heinz mean of two arguments for three or more variables. We...
-
Topological Algebra
When the same set carries both algebraic and topological structure then it is good if they are “compatible”: this usually means that the algebraic...
-
Some remarks on Phelps property U of a Banach space into C(K) spaces
A subspace X of a Banach space Y has Property U whenever every continuous linear functional on X has a unique norm-preserving (i.e., Hahn–Banach)...
-
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...
-
Extreme states on operator spaces in ternary rings of operators
An extension result for rectangular operator extreme states on operator spaces in ternary rings of operators is proved. It is established that for...
-
Banach Space Theory
In this chapter we present some basic concepts and results from Functional Analysis (Banach Space Theory). In Sect. 3.2 we introduce the terminology...
-
Endpoint Functions: Mathematical Apparatus and Economic Applications
AbstractProblems related to the extremization of functions have been studied for quite a long time not only by Russian experts but also by the...
-
Suns, Moons, and \(\mathring{B}\)-complete Sets in Asymmetric Spaces
Classical concepts and problems of geometric approximation theory are considered in normed and asymmetric spaces. Relations between strict suns, sets...
-
Banach Spaces
This chapter deals with what could be called geometric functional analysis. Results from plane geometry are generalized to infinite dimensional...