Banach Lattices
| Main Author: | |
|---|---|
| Format: | eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1991, 1991
|
| Edition: | 1st ed. 1991 |
| Series: | Universitext
|
| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1 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