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Record Nr. |
UNINA9910779725503321 |
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Autore |
Popov Mykhaĭlo Mykhaĭlovych |
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Titolo |
Narrow operators on function spaces and vector lattices [[electronic resource] /] / Mikhail Popov, Beata Randrianantoanina |
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Pubbl/distr/stampa |
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Berlin, : De Gruyter, 2013 |
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ISBN |
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Descrizione fisica |
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1 online resource (336 p.) |
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Collana |
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De Gruyter Studies in Mathematics ; ; 45 |
De Gruyter studies in mathematics, , 0179-0986 ; ; 45 |
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Classificazione |
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Altri autori (Persone) |
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Disciplina |
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Soggetti |
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Narrow operators |
Riesz spaces |
Function spaces |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references and indexes. |
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Nota di contenuto |
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Frontmatter -- Preface -- Contents -- Chapter 1. Introduction and preliminaries -- Chapter 2. Each "small" operator is narrow -- Chapter 3. Some properties of narrow operators with applications to nonlocally convex spaces -- Chapter 4. Noncompact narrow operators -- Chapter 5. Ideal properties, conjugates, spectrum and numerical radii of narrow operators -- Chapter 6. Daugavet-type properties of Lebesgue and Lorentz spaces -- Chapter 7. Strict singularity versus narrowness -- Chapter 8. Weak embeddings of L1 -- Chapter 9. Spaces X for which every operator T ∈ ℒ (Lp;X) is narrow -- Chapter 10. Narrow operators on vector lattices -- Chapter 11. Some variants of the notion of narrow operators -- Chapter 12. Open problems -- Bibliography -- Index of names -- Subject index |
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Sommario/riassunto |
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Most 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 |
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