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The development of dual spaces in functional analysis
What is duality in functional analysis? A way to answer this question is to study the use of this term in functional analysis. One of the first...
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On m-ovoids of finite classical polar spaces with an irreducible transitive automorphism group
In this paper, we classify the m -ovoids of finite classical polar spaces that admit a transitive automorphism group acting irreducibly on the ambient...
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Antinorms and Self-Polar Polyhedra
Antinorms (homogeneous concave functionals on a cone) have many applications in functional analysis, matrix theory, etc. Some duality theory...
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The Classical Spaces
In this chapter, the properties of the main normed spaces are explored:...
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The Dual Brunn–Minkowski Inequalities in Spherical and Hyperbolic Spaces
The dual Brunn–Minkowski inequalities on star bodies in spherical and hyperbolic spaces have been established, together with precise equality...
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Locally Convex Spaces with All Archimedean Cones Closed
We provide an exhaustive description of the class of locally convex spaces in which all Archimedean cones are closed. We introduce the notion of...
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The \(\alpha \) -Bloch Spaces
In this chapter, we mainly study the \(\alpha \) -Bloch...
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Sums of Dual Toeplitz Products on the Orthogonal Complements of the Hardy–Sobolev Spaces
We consider the dual Toeplitz operators acting on the orthogonal complements of Hardy–Sobolev spaces of the unit ball. We first characterize the...
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Hilbert Spaces
Inner products are generalizations of the dot product in $$\mathbb...
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Banach Spaces
This chapter explores the properties of operators and functionals on general Banach spaces, with the aim of generalizing various results on Hilbert...
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Subtransversality and Strong CHIP of Closed Sets in Asplund Spaces
In this paper, we mainly study subtransversality and two types of strong CHIP (given via Fréchet and limiting normal cones) for a collection of...
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On Distinguished Spaces \(C_p(X)\) of Continuous Functions
This survey paper presents a number of recent results related to the study of spaces...
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K-frames for Krein spaces
The aim of this article is to give a definition of K -frames in Krein spaces. This definition is compatible with K -frames already known in Hilbert...
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Noncommutative martingale Hardy-Orlicz spaces: Dualities and inequalities
We investigate dualities and inequalities related to noncommutative martingale Hardy-Orlicz spaces. More precisely, for a concave Orlicz function Φ,...
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The Homogenization Cone: Polar Cone and Projection
Let C be a closed convex subset of a real Hilbert space containing the origin, and assume that K is the homogenization cone of C , i.e., the smallest...
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Symmetric Spaces of \(\tau \) -Measurable Operators
The notion of a bimodule of \(\tau \) -measurable operators...
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Boolean Valued Analysis of Banach Spaces
We implement the Boolean valued analysis of Banach spaces. The realizations of Banach spaces in a Boolean valued universe are lattice normed spaces....