Results 91 to 100 of about 203 (138)

Measures of noncompactness of interpolated polynomials

Forum Mathematicum, 2022
Abstract We study interpolation of the measure of noncompactness of homogeneous polynomials on Banach spaces. We prove that, for a large class of interpolation functors, preserving interpolation of measures of noncompactness of interpolated linear operators between Banach couples can be lifted to polynomials.
Mastyło, Mieczysław, da Silva, Eduardo Brandani   +1 more
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Inequivalent measures of noncompactness

Annali di Matematica Pura ed Applicata, 2010
Let \(X\) be a Banach space and \({\mathcal B}(X)\) denote the set of all bounded subsets of \(X\). We say that a map \(\beta:{\mathcal B}(X)\to [0,\infty)\) is a homogeneous measure of noncompactness on \(X\) if for all \(S,T\in{\mathcal B}(X)\): (1) \(\beta(S)= 0\) iff \(\overline S\) is compact, (2) \(\beta(S)\leq\beta(T)\) for all \(S\subset T ...
Mallet-Paret, John, Nussbaum, Roger D.
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On measures of weak noncompactness

Annali di Matematica Pura ed Applicata, 1988
The authors give an axiomatic definition of measures of weak noncompactness which is in some sense parallel to \textit{B. N. Sadovskij}'s definition of measures of (strong) noncompactness [see e.g. Usp. Mat. Nauk 27, No.1, 81-146 (1972; Zbl 0243.47033)]. The first explicit measure of weak noncompactness is due to \textit{F. S. de Blasi} [Bull.
Banaś, Józef, Rivero, Jesus
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Measures of Noncompactness

1997
As we have seen in Chapter I, compactness plays an essential role in the proof of the Schauder fixed point theorem. However, there are some important problems where the operators are not compact.
J. M. Ayerbe Toledano, T. Domínguez Benavides, G. López Acedo   +2 more
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Measures of Noncompactness

1992
In this chapter we consider the basic notions connected with measures of noncompactness (MNCs for brevity) and condensing (or densifying) operators. We define and study in detail the three main and most frequently used MNCs: the Hausdorff MNC χ the Kuratowski MNC α, and the MNC β.
R. R. Akhmerov, M. I. Kamenskii, A. S. Potapov, A. E. Rodkina, B. N. Sadovskii   +4 more
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Matrix Transformations and Measures of Noncompactness

2021
The major part of this chapter is introductory and included as a reference for the reader’s convenience; it recalls the concepts and results from the theories of sequence spaces, matrix transformations in Sects. 1.1–1.3, and 1.5 and measures of noncompactness in Sects. 1.7–1.10 that are absolutely essential for the book.
Bruno de Malafosse, Eberhard Malkowsky, Vladimir Rakočević   +2 more
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Measure of Noncompactness and Spectral Theory

Mathematische Nachrichten, 1984
Using the theory of measure of noncompactness the author has extended the results of J. Leray on the spectral theory to the case of noncompact operators in Fréchet spaces. Applying these results the author has estimated the radius of the essential spectrum of operators and has obtained some results in operator theory.
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On measures of weak noncompactness

Publicationes Mathematicae Debrecen, 1994
A notion of measure of weak noncompactness is introduced which generalizes the De Blasi measure of weak noncompactness. Some properties of this generalized measure are proved. The existence of bounded weak solutions of certain differential equations is shown.
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Compactness in measure and measure of noncompactness

Siberian Mathematical Journal, 1997
In the class of Banach function spaces with order continuous norm, the author reduces the notion of compactness in measure for a subset of a function space to some equality between two numerical characteristics of the subset.
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Strongly Generated Banach Spaces and Measures of Noncompactness

Mathematische Nachrichten, 1998
AbstractTo generalize the Hausdorff measure of noncompactness to other classes of bounded sets (like e. g. conditionally weakly compact or Asplund sets), we introduce Grothendieck classes. We deduce integral inequalities for quantities (called Grothendieck measures) related to these classes.
Kunze, Markus, Schlüchtermann, Georg
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