A compactness criterion of mixed Krasnoselskiĭ-Riesz type in regular ideal spaces of vector functions

DOI10.4171/ZAA/908zbMath0941.46016MaRDI QIDQ1806191

Martin Väth

Publication date: 20 December 1999

Published in: Zeitschrift für Analysis und ihre Anwendungen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/48480

zbMATH Keywords

Köthe spacecompactness criterionideal spacesHausdorff measure of non-compactnesspreideal space

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Spaces of vector- and operator-valued functions (46E40) Vector-valued measures and integration (46G10) Compactness in Banach (or normed) spaces (46B50)

Related Items (7)

Compactness and Vitali's compactness criterion in vector-valued \(F\)-seminormed function spaces ⋮ On Banach function \(M\)-spaces ⋮ On fixed point theorems and applications to product of n-nonlinear integral operators in ideal spaces ⋮ On a fixed point theorem for the product of operators ⋮ Compactness estimates for integral operators of vector functions with nonmeasurable kernels ⋮ The dual space of \(L_\infty\) is \(L_1\) ⋮ On some fixed point theorems in abstract duality pairs

Cites Work

• On the Cauchy problem for ordinary differential equations in Banach spaces
• Geometry of Banach spaces. Selected topics
• Compactness and existence results for ordinary differential equations in Banach spaces
• On measures of non-compactness in regular spaces
• The structure of weakly compact sets in Banach spaces
• On the behaviour of measures of noncompactness with respect to differentiation and integration of vector-valued functions
• On the structure of $L_{φ}$-solution sets of integral equations in Banach spaces
• Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces
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