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Introduction to the Theory of Bases

Author: Jürg T Marti
Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 1969.
Series: Springer tracts in natural philosophy, 18.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
Since the publication of Banach's treatise on the theory of linear operators, the literature on the theory of bases in topological vector spaces has grown enormously. Much of this literature has for its origin a question raised in Banach's book, the question whether every sepa rable Banach space possesses a basis or not. The notion of a basis employed here is a generalization of that of a Hamel basis for a finite  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Jürg T Marti
ISBN: 9783642871405 3642871402
OCLC Number: 851389336
Description: 1 online resource (xii, 151 pages).
Contents: I. Linear Transformations --
1. Linear Topological Spaces --
2. Linear Transformations --
3. Conjugate Spaces and Weak Topologies --
4. Special Banach Spaces --
II Convergence of Series in Banach Spaces --
1. Relations among Different Types of Convergence --
2. Unconditional and Absolute Convergence --
III. Bases for Banach Spaces --
1. Bases Corresponding to Different Topologies --
2. Biorthogonal Systems --
3. Shrinking and Boundedly Complete Bases --
4. Unconditional Bases --
5. Absolutely Convergent Bases and Uniform Bases --
6. T-Bases --
7. Bases for Special Spaces --
IV. Orthogonality, Projections and Equivalent Bases --
1. Bases and Projections --
2. Orthogonality, simple N1-Spaces and Monotone Bases --
3. Equivalent Bases --
V. Bases and Structure of the Space --
1. Bases, Completeness and Separability --
2. Bases and Reflexivity --
3. Criteria for Finite Dimension --
VI. Bases for Hilbert Spaces --
1. Monotone and Orthonormal Bases --
2. Unconditional Bases for Hilbert Spaces --
VII. Decompositions --
1. Decompositions of F-Spaces --
2. Decompositions of Banach Spaces --
VIII. Applications to the Theory of Banach Algebras --
1. Two-Sided Ideals of Operators of Finite Rank --
2.?-Rings --
3. Proper?-Rings of Schauder Decompositions --
4. Minimal Schauder Decompositions --
5. Banach Algebras and Unconditional Bases --
IX. Some Results on Generalized Bases for Linear Topological Spaces --
1. Definition and Fundamental Properties of Generalized Bases --
2. Dual Generalized Bases --
3. Examples --
4. Similar Bases --
5. Continuity of the Coefficient Functionals --
Author and Subject Index.
Series Title: Springer tracts in natural philosophy, 18.
Responsibility: by Jürg T. Marti.

Abstract:

Since the publication of Banach's treatise on the theory of linear operators, the literature on the theory of bases in topological vector spaces has grown enormously. Much of this literature has for  Read more...

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