Author | Marti, Jรผrg T. author |
---|---|
Title | Introduction to the Theory of Bases [electronic resource] / by Jรผrg T. Marti |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1969 |
Connect to | http://dx.doi.org/10.1007/978-3-642-87140-5 |
Descript | XII, 151 p. online resource |
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