A compactness criterion for translation invariant Banach spaces of functions

DOI10.1007/BF02199925zbMath0515.46043MaRDI QIDQ1051858

Hans G. Feichtinger

Publication date: 1982

Published in: Analysis Mathematica (Search for Journal in Brave)

zbMATH Keywords

compactnessBanach function spacetightnesstightequicontinuousbounded approximate units with compact supportcompactness of a closed bounded subset in a Banach space of locally integrable functions on a locally compact groupsRiesz-Kolmogorov-Weil compactness criterion

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) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX) (46H25) (L^p)-spaces and other function spaces on groups, semigroups, etc. (43A15) Compactness in topological linear spaces; angelic spaces, etc. (46A50)

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Cites Work

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• On a class of convolution algebras of functions
• A note on the Voronoi summation formula
• Translation invariant operators in \(L^ p\)
• \(L^ 1\)-algebras and Segal algebras
• Segal Algebras and Left Normed Ideals