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Measures of Noncompactness in Regular Spaces

  • Nina A. Erzakova,
    Moscow State Technical University of Civil Aviation
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Abstract

Previous results by the author on the connection between three of measures of non-compactness obtained for $L_p$, are extended to regular spaces of measurable functions. An example of advantage in some cases one of them in comparison with another is given. Geometric characteristics of regular spaces are determined. New theorems for $(k,\beta)$-boundedness of partially additive operators are proved.
Keywords: measure of non-compactness, condensing map, partially additive operator, regular space, ideal space measure of non-compactness, condensing map, partially additive operator, regular space, ideal space
MSC Classifications: 47H08, 46E30, 47H99, 47G10 show english descriptions Measures of noncompactness and condensing mappings, $K$-set contractions, etc.
Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Kothe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
None of the above, but in this section
Integral operators [See also 45P05]
47H08 - Measures of noncompactness and condensing mappings, $K$-set contractions, etc.
46E30 - Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Kothe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
47H99 - None of the above, but in this section
47G10 - Integral operators [See also 45P05]
 

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