LEADER 04242nam 2200745 a 450 001 9910779725503321 005 20200520144314.0 010 $a3-11-026334-3 024 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(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$b[electronic resource] /$fMikhail Popov, Beata Randrianantoanina 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 $a3-11-026303-3 311 $a1-299-71911-2 320 $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 610 $aFunction Space. 610 $aNarrow Operator. 610 $aVector Lattice. 615 0$aNarrow operators. 615 0$aRiesz spaces. 615 0$aFunction spaces. 676 $a515/.73 686 $aSK 600$2rvk 700 $aPopov$b Mykhai?lo Mykhai?lovych$01469010 701 $aRandrianantoanina$b Beata$0518410 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910779725503321 996 $aNarrow operators on function spaces and vector lattices$93680413 997 $aUNINA