LEADER 04660nam 22005655 450 001 9910962860503321 005 20250813223431.0 010 $a3-642-76724-9 024 7 $a10.1007/978-3-642-76724-1 035 $a(CKB)3400000000107806 035 $a(SSID)ssj0000805253 035 $a(PQKBManifestationID)11425184 035 $a(PQKBTitleCode)TC0000805253 035 $a(PQKBWorkID)10835566 035 $a(PQKB)11744982 035 $a(DE-He213)978-3-642-76724-1 035 $a(MiAaPQ)EBC3096209 035 $a(PPN)23801777X 035 $a(BIP)9557764 035 $a(EXLCZ)993400000000107806 100 $a20121227d1991 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aBanach Lattices /$fby Peter Meyer-Nieberg 205 $a1st ed. 1991. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d1991. 215 $a1 online resource (XV, 395 p.) 225 1 $aUniversitext,$x2191-6675 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a3-540-54201-9 320 $aIncludes bibliographical references and index. 327 $a1 Riesz Spaces -- 1.1 Basic Properties of Riesz Spaces and Banach Lattices -- 1.2 Sublattices, Ideals, and Bands -- 1.3 Regular Operators and Order Bounded Functionals -- 1.4 Duality of Riesz Spaces, the Nakano Theory -- 1.5 Extensions of Positive Operators -- 2 Classical Banach Lattices -- 2.1 C(K)-Spaces and M-Spaces -- 2.2 Complex Riesz Spaces -- 2.3 Disjoint Sequences and Approximately Order Bounded Sets -- 2.4 Order Continuity of the Norm, KB-Spaces and the Fatou Property -- 2.5 Weak Compactness -- 2.6 Banach Function Spaces -- 2.7 Lp-Spaces and Related Results -- 2.8 Cone p-Absolutely Summing Operators and p-Subadditive Norms -- 3 Operators on Riesz Spaces and Banach Lattices -- 3.1 Disjointness Preserving Operators and Orthomorphisms on Riesz Spaces -- 3.2 Operators on L-and M-Spaces -- 3.3 Kernel Operators -- 3.4 Order Weakly Compact Operators -- 3.5 Weakly Compact Operators -- 3.6 Approximately Order Bounded Operators -- 3.7 Compact Operators and Dunford-Pettis Operators -- 3.8 Tensor Products of Banach Lattices -- 3.9 Vector Measures and Vectorial Integration -- 4 Spectral Theory of Positive Operators -- 4.1 Spectral Properties of Positive Linear Operators -- 4.2 Irreducible Operators -- 4.3 Measures of Non-Compactness -- 4.4 Local Spectral Theory for Positive Operators -- 4.5 Order Spectrum of Regular Operators -- 4.6 Disjointness Preserving Operators and the Zero-Two Law -- 5 Structures in Banach Lattices -- 5.1 Banach Space Properties of Banach Lattices -- 5.2 Banach Lattices with Subspaces Isomorphic to C(?), C(0,l), and L1(0,1) -- 5.3 Grothendieck Spaces -- 5.4 Radon-Nikodym Property in Banach Lattices -- References. 330 $aThis book is mainly concerned with the theory of Banach lattices and with linear operators defined on, or with values in Banach lattices. Moreover we will always consider more general classes of Riesz spaces so long as this does not involve more complicated constructions or proofs. In particular, we will not treat any phenomena which occur only in the non-Banach lattice situation. Riesz spaces, also called vector lattices, K-lineals, are linear lattices which were first considered by F. Riesz, 1. Kantorovic, and H. Freudenthal. Subse­ quently other important contributions came from the Soviet Union (L.V. Kan­ torovic, A.J. Judin, A.G. Pinsker, and B.Z. Vulikh), Japan (H. Nakano, T. Oga­ sawara, and K. Yosida), and the United States (G. Birkhoff, H.F. Bohnenblust, S. Kakutani, and M.l\f. Stone). In the last twenty-five years the theory rapidly increased. Important con­ tributions came from the Dutch school (W.A.J. Luxemburg, A.C. Zaanen) and the Tiibinger school (lI.lI. Schaefer). In the middle seventies the research on this subject was essentially influenced by the books of H.H. Schaefer (1974) and W.A.J. Luxemburg and A.C. Zaanen (1971). More recently other impor­ tant books concerning this subject appeared, A.C. Zaanen (1983), H.U. Schwarz (1984), and C.D. Aliprantis and O. Burkinshaw (1985). 410 0$aUniversitext,$x2191-6675 606 $aFunctions of real variables 606 $aReal Functions 615 0$aFunctions of real variables. 615 14$aReal Functions. 676 $a512/.55 700 $aMeyer-Nieberg$b Peter$4aut$4http://id.loc.gov/vocabulary/relators/aut$059489 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910962860503321 996 $aBanach lattices$983019 997 $aUNINA