Canad. Math. Bull. 57(2014), 780-793
Printed: Dec 2014
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
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.
measure of non-compactness, condensing map, partially additive operator, regular space, ideal space
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]