Narrow operators on function spaces and vector lattices

Narrow operators on function spaces and vector lattices / by Mikhail Popov, Beata Randrianantoanina.

"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 orig...

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Bibliographic Details
Main Author: Popov, Mykhaĭlo Mykhaĭlovych (Author)
Other Authors: Randrianantoanina, Beata
Format: eBook
Language:English
Published: Berlin : De Gruyter, [2013]
Series:De Gruyter studies in mathematics ; 45.
Subjects:
Narrow operators.
Riesz spaces.
Function spaces.
MATHEMATICS > Transformations.
Function spaces
Narrow operators
Riesz spaces
Online Access:Click for online access
Table of Contents:
  • Introduction and preliminaries
  • Each "small" operator is narrow
  • Applications to nonlocally convex spaces
  • Noncompact narrow operators
  • Ideal properties, conjugates, spectrum and numerical radii
  • Daugavet-type properties of Lebesgue and Lorentz spaces
  • Strict singularity versus narrowness
  • Weak embeddings of L1
  • Spaces X for which every operator T L(Lp, X) is narrow
  • Narrow operators on vector lattices
  • Some variants of the notion of narrow operators
  • Open problems.

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