Finite Elements in Vector Lattices

Name: Finite Elements in Vector Lattices
Brand: De Gruyter
Price: 189.95 EUR
Availability: OnlineOnly

Martin R. Weber(Autor*in)

De Gruyter (Verlag)

1. Auflage

Erschienen am 20. August 2014

IX, 220 Seiten

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Inhalt

Intro
Contents
1. Introduction
2. Ordered vector spaces and vector lattices
2.1 Ordered vector spaces and positive operators
2.2 Vector lattices
2.3 Ordered normed spaces
2.4 Normed Riesz spaces and Banach lattices
2.5 Representation of Banach lattices
3. Finite, totally finite and selfmajorizing elements
3.1 Finite and totally finite elements in vector lattices
3.2 Finite elements in Banach lattices
3.3 Finite elements in sublattices and in direct sums of Banach lattices
3.3.1 Finite elements in sublattices
3.3.2 Finite elements in the bidual of Banach lattices
3.3.3 Finite elements in direct sums of Banach lattices
3.4 Selfmajorizing elements in vector lattices
3.4.1 The order ideal of all selfmajorizing elements in a vector lattice
3.4.2 General properties of selfmajorizing elements
3.4.3 Examples of selfmajorizing elements
3.5 Finite elements in l-algebras and in product algebras
3.5.1 Lattice ordered algebras
3.5.2 Finite elements in unitary l-algebras
3.5.3 Finite elements in nonunitary f-algebras
3.5.4 Finite elements in product algebras
4. Finite elements in vector lattices of linear operators
4.1 Some general results
4.2 Finiteness of regular operators on AL-spaces
4.3 Finite rank operators in the vector lattice of regular operators
4.4 Some vector lattices and Banach lattices of operators
4.4.1 Vector lattices of operators
4.4.2 Banach lattices of operators
4.5 Operators as finite elements
4.6 Finite rank operators as finite elements
4.7 Impact of the order structure of V(E, F) on the lattice properties of E and F
5. The space of maximal ideals of a vector lattice
5.1 Representation of vector lattices by means of extended real continuous functions
5.2 Maximal ideals and discrete functionals
5.3 The topology on the space of maximal ideals of a vector lattice
5.4 The Hausdorff property of M
6. Topological characterization of finite elements
6.1 Topological characterization of finite, totally finite and selfmajorizing elements
6.1.1 The canonical map and the conditional representation
6.1.2 Topological characterization of finite elements
6.1.3 Topological characterization of totally finite elements
6.1.4 Topological characterization of selfmajorizing elements
6.2 Relations between the ideals of finite, totally finite and selfmajorizing elements
6.3 The topological spaceMfor vector lattices of type (S)
6.4 Examples
7. Representations of vector lattices and their properties
7.1 A classification of representations and the standard map
7.2 Vector lattices of type (S) and their representations
8. Vector lattices of continuous functions with finite elements
8.1 Vector lattices of continuous functions with many finite functions
8.2 Finite elements in vector lattices of continuous functions
8.3 An isomorphism result for vector lattices of continuous functions
9. Representations of vector lattices by means of continuous functions
9.1 Representations which contain finite functions
9.2 The existence of Fa- representations for vector lattices of type (S)
9.3 LF-vector lattices
9.4 Vector lattices of type (CM)
10. Representations of vector lattices by means of bases of finite elements
10.1 Bases of finite elements and a -representations
10.2 Representations by means of R-bases of finite elements
10.3 Some properties of the realization space
List of Examples
List of Symbols
Bibliography
Index

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