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Local Theory of Optimization
In this chapter, we derive the local necessary, as well as sufficient conditions for the unconstrained optimization of a functional, the constrained...
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Banach Spaces Which are Isometric to Subspaces of c0(Γ)
In this paper, we give a number of characterizations for a Banach space X which is isometric to a subspace of c 0 , or, c 0 (Γ), successively, in terms...
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States and Representations
A positive linear functional on a C∗-algebra is one that takes positive elements to non-negative numbers. They are automatically bounded, and among...
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Equivalent norms
In this chapter we discuss the basic notion of an equivalent norm (Definition 2 above) in Section 3.1, and for finite-dimensional spaces, in Section...
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Types of von Neumann Algebras
The classification of von Neumann algebras requires a good understanding of their orthogonal projections. We show that they form a complete lattice...
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On Perturbed Isometries Between the Positive Cones of Certain Continuous Function Spaces
Let X , Y be two compact Hausdorff perfectly normal spaces (in particular, compact metrizable spaces), C ( X ) be the real Banach space of all continuous...
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Riemann Surfaces
A Riemann surface is a differentiable manifold with charts in \( \mathbb{C} \)...
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On a Set of Norm Attaining Operators and the Strong Birkhoff–James Orthogonality
Continuing the study of recent results on the Birkhoff–James orthogonality and the norm attainment of operators, we introduce a property namely the...
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Regularity of the Semigroup of Regular Probability Measures on Locally Compact Hausdorff Topological Groups
Let G be a locally compact Hausdorff group, and let P ( G ) denote the class of all regular probability measures on G . It is well known that P ( G ) forms...
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The Space of Bounded Operators on a Hilbert Space as Ordered Vector Space
This chapter is a study of the space of bounded operators on any complex Hilbert space as a pedagogical model of C∗-algebra. We explain in particular...
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Guaranteed Deterministic Approach to Superhedging: Most Unfavorable Scenarios of Market Behavior and the Moment Problem
AbstractWe consider a guaranteed deterministic problem setting of discrete-time superreplication: the aim of hedging of a contingent claim is to...
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Diversity of Lorentz-Zygmund Spaces of Operators Defined by Approximation Numbers
We prove the following dichotomy for the spaces ℒ
p , q , α ( a ) ( X , Y ) of all operators T ∈ ℒ ( X , Y ) whose approximation numbers belong to the... -
Classes of Harmonic Functions Defined By the Extended SăLăgean Operator
We investigate the classes of harmonic functions defined by the extended Sălăgean operator. By using the theory of extreme points, we obtain the...
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Von Neumann algebras and irreducible representations
For any Hilbert space H, the bounded operators B(H) admit topologies distinct the norm topology. We will be interested in the weak operator and the...