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Compatible results on boundedness of matrix operators on weighted Copson sequence spaces
In this paper, we study the boundedness of the matrix operators from weighted sequence spaces into Copson weighted sequence spaces and deduce several...
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Sequence Spaces Inclusion Equations
In this chapter, we consider new problems of perturbations with exercises on sequence spaces and determine the sets of all the solutions of special...
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Closures of Holomorphic Tent Spaces in Weighted Bloch Spaces
In this paper, we characterize the closures of holomorphic tent spaces in weighted Bloch spaces in terms of natural level sets, where the holomorphic...
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Some new observations on Catalan almost convergent sequence spaces and the Catalan core
k]In this article, we introduce and study Catalan almost convergent sequence spaces by using the Catalan matrix. We obtain topological properties and...
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On some classes of compact and matrix operators on the generalized weighted mean difference sequence spaces of fractional order
Recently, the generalized weighted mean difference operator of fractional order and related sequence spaces were introduced and studied by Nayak et...
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Optimal embeddings for Triebel–Lizorkin and Besov spaces on quasi-metric measure spaces
In this article, via certain lower bound conditions on the measures under consideration, the authors fully characterize the Sobolev embeddings for...
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Hilbert Spaces
Inner products are generalizations of the dot product in $$\mathbb...
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Mean Ergodic Weighted Shifts on Köthe Echelon Spaces
Necessary and sufficient conditions are given for mean ergodicity, power boundedness, and topologizability for weighted backward shift and weighted...
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Fourier Transform of Anisotropic Hardy Spaces Associated with Ball Quasi-Banach Function Spaces and Its Applications to Hardy-Littlewood Inequalities
Let A be a general expansive matrix and X be a ball quasi-Banach function space on ℝ n , whose certain power (namely its convexification) supports a...
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Grand Sobolev Spaces on Metric Measure Spaces
We study the properties of the so-called grand Sobolev spaces on a metric measure space. The introduction of the spaces is motivated by the available...
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Local Korovkin-type approximation problems for bounded function spaces
The paper is concerned with some local approximation problems by special classes of positive linear operators acting on spaces of Borel measurable...
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The Classical Spaces
In this chapter, the properties of the main normed spaces are explored:...
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Metric Spaces
In the previous chapters, we have introduced the concept of topological space, as well as a variety of concepts related to proximity. Following our...
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Hybrid Maximal Filter Spaces
We introduce a new way of encoding general topology in second order arithmetic that we call hybrid maximal filter (hybrid MF) spaces. This notion is...
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Models of Self-Adjoint and Unitary Operators in Pontryagin Spaces
This article is a revised version of the lectures given by the author at KROMSH-2019. These lectures are devoted to describing a few different ways...
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Universal Spaces
The Urysohn space is the main hero of this lecture. It shares some fundamental properties with classical spaces (spheres, Euclidean, and Lobachevsky...
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Variable Besov-type Spaces
In this paper we introduce Besov-type spaces with variable smoothness and integrability. We show that these spaces are characterized by the...
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Lebesgue Spaces
The most well-known example of a linear space is the Euclidean spaces \(\mathbb {R}^{n}\)...