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Banach Lattices (Universitext) - Softcover

 
9783540542018: Banach Lattices (Universitext)
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This book is concerned primarily with the theory of Banach lattices and with linear operators defined on, or with values in, Banach lattices. More general classes of Riesz spaces are considered so long as this does not lead to more complicated constructions or proofs. The intentions for writing this book were twofold. First, there appeared in the literature many results completing the theory extensively. On the other hand, new techniques systematically applied here for the first time lead to surprisingly simple and short proofs of many results originally known as deep. These new methods are purely elementary: they directly yield the Banach lattice versions of theorems which then include the classical theorems in a trivial manner. In particular the book covers: Riesz spaces, normed Riesz spaces, C(K)-and Mspaces, Banach function spaces, Lpspaces, tensor products of Banach lattices, Grothendieck spaces; positive and regular operators, extensions of positive operators, disjointness-preserving operators, operators on L- and M-spaces, kernel operators, weakly compact operators and generalizations, Dunford-Pettis operators and spaces, irreducible operators; order continuity of norms, p-subadditive norms; spectral theory, order spectrum; embeddings of C; the Radon-Nikodym property; measures of non-compactness. This textbook on functional analysis, operator theory and measure theory is intended for advanced students and researchers.

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  • PublisherSpringer
  • Publication date1991
  • ISBN 10 3540542019
  • ISBN 13 9783540542018
  • BindingPaperback
  • Number of pages410

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Book Description Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This 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.lf. 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). 416 pp. Englisch. Seller Inventory # 9783540542018

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Book Description Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 1 Riesz Spaces.- 1.1 Basic Properties of Riesz Spaces and Banach Lattices.- Elementary Properties of Ordered Spaces.- Elementary Properties of Riesz Spaces.- Normed Riesz Spaces, Definition.- Order-Completeness Properties of Riesz Spaces.- Order Convergence. Seller Inventory # 4893099

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Book Description Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - This 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.lf. 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). Seller Inventory # 9783540542018

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