Results 251 to 260 of about 123,114 (281)

Measures of Non-Compactness and Sobolev–Lorentz Spaces

Zeitschrift für Analysis und ihre Anwendungen, 2020
We show that the measure of non-compactness of the limiting embedding of Sobolev–Lorentz spaces is equal to the norm. This is a consequence of our general theorem for arbitrary Banach spaces.
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Measures of Non-compactness

2014
The degree of non-compactness of a set is measured by means of functions called measures of non-compactness. In this chapter we study the three main and most frequently used measures of non-compactness (MNCs).
Józef Banaś, Mohammad Mursaleen
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KURATOWSKI'S MEASURE OF NON-COMPACTNESS REVISITED

The Quarterly Journal of Mathematics, 1988
The author earlier introduced the category of approach spaces with contractions, which contains the topological spaces with continuous maps as a bireflective and bicoreflective subcategory and the extended pseudo- quasi-metric spaces with non-expansive maps as a bicoreflective subcategory. A measure of non-compactness is defined for approach spaces and
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Measures of weak non-compactness in 𝐿₁(𝜇)-spaces

Proceedings of the American Mathematical Society, 2023
Disjoint sequence methods from the theory of Riesz spaces are used to study measures of weak non-compactness in L 1 ( μ ) L_{1}(\mu ) -spaces. A principal new result of the present paper is the following: Let E E be an abstract M M
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On Measures of Non-Compactness in Regular Spaces

Zeitschrift für Analysis und ihre Anwendungen, 1996
Previous results on non-compactness obtained in [11–13] are extended to regular spaces of measurable functions, and new criteria for the \mu -compactness of sets and operators are proved.
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On measures of non-compactness and applications to embeddings

Nonlinear Analysis: Theory, Methods & Applications, 1997
The author discusses the compactness and noncompactness of imbeddings between Orlicz spaces and weighted Sobolev spaces. Important tools are capacity estimates and special measures of noncompactness studied in the author's previous work [see e.g. Z. Anal. Anwend. 15, No. 2, 299-307 (1996; Zbl 0849.47031)].
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Measures of non–compactness of classical embeddings of Sobolev spaces

Mathematische Nachrichten, 2003
AbstractLet Ω be an open subset of ℝn and let p ∈ [1, n). We prove that the measure of non–compactness of the Sobolev embedding Wk,p0(Ω) → Lp*(Ω) is equal to its norm. This means that the entropy numbers of this embedding are constant and equal to the norm.
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A Viewpoint to Measure of Non-Compactness of Operators in Banach Spaces

Acta Mathematica Scientia, 2020
In this article, among other things the author investigated the representation of the measure of non-compactness of operators in Banach spaces.
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Remarks on Interpolation Properties of the Measure of Weak Non ‐‐ Compactness and Ideal Variations

Mathematische Nachrichten, 1999
AbstractWe estimate the ideal measure of certain interpolated operators in terms of the measure of their restrictions to the intersection. The dual situation is also studied. Special attention is paid to the ideal of weakly compact operators.
Cobos, Fernando, Martínez, Antón
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15.—The Measure of Non-compactness of Some Linear Integral Operators

Proceedings of the Royal Society of Edinburgh. Section A. Mathematical and Physical Sciences, 1973
SynopsisThe measure of non-compactness of linear integral operators on the half-line [0, ∞) of a special type is studied. In particular, a necessary and sufficient condition is established for an operator of this type to define a compact operator from L2(0, ∞) into itself. These results are then used to discuss the spectrum of second-order differential
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