LEADER 04159nam 2200757 a 450 001 9911131985303321 005 20260415140134.0 010 $a9783110263343 010 $a3110263343 024 7 $a10.1515/9783110263343 035 $a(CKB)2550000001096628 035 $a(EBL)893867 035 $a(OCoLC)826479699 035 $a(SSID)ssj0000833721 035 $a(PQKBManifestationID)11411976 035 $a(PQKBTitleCode)TC0000833721 035 $a(PQKBWorkID)10936099 035 $a(PQKB)10164674 035 $a(MiAaPQ)EBC893867 035 $a(DE-B1597)172141 035 $a(OCoLC)853248751 035 $a(OCoLC)987750987 035 $a(DE-B1597)9783110263343 035 $a(Au-PeEL)EBL893867 035 $a(CaPaEBR)ebr10649212 035 $a(CaONFJC)MIL503162 035 $a(PPN)175558302 035 $a(Perlego)653116 035 $a(EXLCZ)992550000001096628 100 $a20121026d2013 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aNarrow operators on function spaces and vector lattices /$fMikhail Popov, Beata Randrianantoanina 205 $a1st ed. 210 $aBerlin $cDe Gruyter$d2013 215 $a1 online resource (336 p.) 225 0 $aDe Gruyter Studies in Mathematics ;$v45 225 0$aDe Gruyter studies in mathematics,$x0179-0986 ;$v45 300 $aDescription based upon print version of record. 311 08$a9783110263039 311 08$a3110263033 311 08$a9781299719118 311 08$a1299719112 320 $aIncludes bibliographical references and indexes. 327 $t Frontmatter -- $tPreface -- $tContents -- $tChapter 1. Introduction and preliminaries -- $tChapter 2. Each "small" operator is narrow -- $tChapter 3. Some properties of narrow operators with applications to nonlocally convex spaces -- $tChapter 4. Noncompact narrow operators -- $tChapter 5. Ideal properties, conjugates, spectrum and numerical radii of narrow operators -- $tChapter 6. Daugavet-type properties of Lebesgue and Lorentz spaces -- $tChapter 7. Strict singularity versus narrowness -- $tChapter 8. Weak embeddings of L1 -- $tChapter 9. Spaces X for which every operator T ? ? (Lp;X) is narrow -- $tChapter 10. Narrow operators on vector lattices -- $tChapter 11. Some variants of the notion of narrow operators -- $tChapter 12. Open problems -- $tBibliography -- $tIndex of names -- $tSubject index 330 $aMost classes of operators that are not isomorphic embeddings are characterized by some kind of a "smallness" condition. Narrow operators are those operators defined on function spaces that are "small" at {-1,0,1}-valued functions, e.g. compact operators are narrow. The original motivation to consider such operators came from theory of embeddings of Banach spaces, but since then they were also applied to the study of the Daugavet property and to other geometrical problems of functional analysis. The question of when a sum of two narrow operators is narrow, has led to deep developments of the theory of narrow operators, including an extension of the notion to vector lattices and investigations of connections to regular operators. Narrow operators were a subject of numerous investigations during the last 30 years. This monograph provides a comprehensive presentation putting them in context of modern theory. It gives an in depth systematic exposition of concepts related to and influenced by narrow operators, starting from basic results and building up to most recent developments. The authors include a complete bibliography and many attractive open problems. 410 3$aDe Gruyter Studies in Mathematics 606 $aNarrow operators 606 $aRiesz spaces 606 $aFunction spaces 615 0$aNarrow operators. 615 0$aRiesz spaces. 615 0$aFunction spaces. 676 $a515/.73 686 $aSK 600$2rvk 700 $aPopov$b Mykhai?lo Mykhai?lovych 701 $aRandrianantoanina$b Beata 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911131985303321 997 $aUNINA