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The Daugavet Equation: Linear and Nonlinear Recent Results
A bounded linear operator \( T:\mathcal{X}\to \mathcal{X} \)...
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Daugavet property in projective symmetric tensor products of Banach spaces
We show that all the symmetric projective tensor products of a Banach space X have the Daugavet property provided X has the Daugavet property and...
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The Lipschitz-Free Space Over a Length Space is Locally Almost Square but Never Almost Square
We prove that the Lipschitz-free space over a metric space M is locally almost square whenever M is a length space. Consequently, the Lipschitz-free...
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Diameter two properties in some vector-valued function spaces
We introduce a vector-valued version of a uniform algebra, called the vector-valued function space over a uniform algebra. The diameter two...
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On a generalisation of Local Uniform Rotundity
In this paper we investigate the property (HLUR), a generalisation of (LUR) property of a Banach space. A Banach space having the property (HLUR) is...
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On the Lipschitz numerical index of Banach spaces
In this article, we investigate further on the Lipschitz numerical radius and index which were recently introduced. First, we provide some renorming...
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Banach spaces which always produce octahedral spaces of operators
We characterise those Banach spaces X which satisfy that L ( Y , X ) is octahedral for every non-zero Banach space Y . They are those satisfying that, for...
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Weakly compactly generated spaces and their relatives III
Projectional resolutions of the identity were a fundamental tool for elucidating the structure of WCG spaces, and one of the fundamental...
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A characterization of Banach spaces containing ℓ1(κ) via ball-covering properties
In 1989, G. Godefroy proved that a Banach space contains an isomorphic copy of ℓ 1 if and only if it can be equivalently renormed to be octahedral. It...
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Operator Norm Attainment
Linear operators lie at the very heart of functional analysis and operator theory. As mentioned in the Preface, this monograph aims at exploring the...
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Stability of diametral diameter two properties
We prove that the diametral diameter two properties are inherited by F -ideals (e.g., M -ideals). On the other hand, these properties are lifted from...
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Three Definitions for Operators: Spearness, the Alternative Daugavet Property, and Lushness
This is the main chapter of our manuscript, as we introduce and deeply study the main definitions: the one of spear operator, the weaker of operator...
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Generalized Polynomial Method for Solving a Cauchy-Type Problem for one Fractional Differential Equation
In this paper, we examine a Cauchy-type problem for one ordinary differential equation with Riemann–Liouville fractional derivatives. For this...