Narrow Operators on Function Spaces and Vector Lattices /

Narrow Operators on Function Spaces and Vector Lattices / / Mikhail Popov, Beata Randrianantoanina.

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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 conside...

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Bibliographic Details
Superior document:Title is part of eBook package: De Gruyter DG Studies in Mathematics eBook-Package
VerfasserIn:
Popov, Mikhail,
Randrianantoanina, Beata,
Place / Publishing House:Berlin ;, Boston : : De Gruyter, , [2012]
©2012
Year of Publication:2012
Language:English
Series:De Gruyter Studies in Mathematics , 45
Online Access:
Physical Description:1 online resource (319 p.)
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Table of Contents:
  • 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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