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Remarks on “some fixed point theorems for s-convex subsets in p-normed spaces”
We explain why a recent proof of Schauder’s conjecture is not correct. A counterexample to a cited intermediate lemma is given.
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Generalizations of Starlike Harmonic Functions Defined by Sălăgean and Ruscheweyh Derivatives
We investigate some generalizations of the classes of harmonic functions defined by the Sălăgean and Ruscheweyh derivatives. By using the...
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On de Finetti-Type Theorems
The investigation of distributional symmetries was initiated by de Finetti’s celebrated theorem, which shows that any finite joint-distribution of...
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A Unifying Representer Theorem for Inverse Problems and Machine Learning
Regularization addresses the ill-posedness of the training problem in machine learning or the reconstruction of a signal from a limited number of...
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Topology on Banach Spaces
It has been shown that the dual spaceDual space of a normed spaceNormed space is complete. Moreover, we have demonstrated some important results...
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Linear map**s on ordered vector spaces
Before we can start to analyze the generalized Riccati operators derived in the previous chapter, we have to deal with generalized Lyapunov operators...
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James boundaries
James boundaries are one of the most important and powerful concepts in Banach space theory. They lead us to many geometrical results. They are the...
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Invariant Banach Limits and Their Convex Subsets
AbstractSets of Banach limits invariant under dilation operators are studied. The convexity of such sets is investigated. Minimal subsets are...
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Lyapunov Convexity Theorem for von Neumann Algebras and Jordan Operator Structures
We establish Lyapunov type theorems on automatic convexity of various affine transformations of the set of extreme points of important convex sets...
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Tropical Reproducing Kernels and Optimization
Hilbertian kernel methods and their positive semidefinite kernels have been extensively used in various fields of applied mathematics and machine...
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Order theoretical structures in atomic JBW-algebras: disjointness, bands, and centres
Every atomic JBW-algebra is known to be a direct sum of JBW-algebra factors of type I. Extending Kadison’s anti-lattice theorem, we show that each of...
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Sobolev Embeddings for Fractional Hajłasz-Sobolev Spaces in the Setting of Rearrangement Invariant Spaces
We obtain symmetrization inequalities in the context of Fractional Hajłasz-Sobolev spaces in the setting of rearrangement invariant spaces and prove...
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The Radon–Nikodým property
The Radon–Nikodým property was introduced in Definition 61 above by using the concept of strongly exposed point. The following is the traditional...
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Convex Sets
Recall that a convex set \(C \subset \mathcal {R}^d\) is a...
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Applications
As we know, one of the main goals of this book has been to find a parametrization of the unit sphere of spaces of polynomials endowed with different...
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Orthogonality for Biadjoints of Operators
Let X, Y be non-reflexive Banach spaces. Let \({\mathcal L}(X,Y)\)...