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Almost‐compact embeddings
Author(s) -
Slavíková Lenka
Publication year - 2012
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201100286
Subject(s) - mathematics , embedding , compact space , almost everywhere , lorentz space , measure (data warehouse) , pure mathematics , function space , lorentz transformation , banach space , locally compact space , product (mathematics) , compact operator , convergence (economics) , relatively compact subspace , space (punctuation) , extension (predicate logic) , computer science , physics , geometry , classical mechanics , database , artificial intelligence , economics , programming language , economic growth , operating system
We study almost‐compact embeddings between Banach function spaces. We prove a necessary and sufficient condition in terms of almost‐everywhere convergence. We also study the dependence of an almost‐compact embedding on the measure space. We introduce a certain product operator and show its intimate relation to an almost‐compact embedding. We also characterize general almost‐compact embeddings among Lorentz and Marcinkiewicz endpoint spaces.