Details

Autor(en) / Beteiligte

• Wilansky, Albert

Titel

Summability through functional analysis [electronic resource]

Link zum Volltext

• Elsevier Books AutoHoldings

Beschreibungen/Notizen

• Description based upon print version of record.
• Includes bibliographical references (p. 303-308) and index.
• Front Cover; Sumability through Functional Analysis; Copyright Page; CONTENTS; CHAPTER 1. MATRICES; 1.0. Functional analysis; 1.1. Introduction; 1.2. Notation; 1.3. Conservative and regular; 1.4. Associativity; 1.5. The algebras G and ?; 1.6. Coregular and conull matrices; 1.7. Types of summability theorems; 1.8. Inverses; CHAPTER 2. CLASSICAL MATRICES; 2.0. Background; 2.1. Introduction; 2.2. Holder matrices; 2.3. Hausdorff matrices; 2.4. Cesáro and Holder; 2.5. Nõ'rlund matrices; 2.6. Polynomial matrices; CHAPTER 3. TRIANGLES AND BANACH SPACE; 3.0. Functional analysis; 3.1. Historical
• 3.2. Convergence domain3.3. The perfect part; 3.4. When c is closed; 3.5. Bounded sequences and non-triangles; CHAPTER 4. FK SPACES; 4.0. Functional Analysis; 4.1. Introduction; 4.2. FK spaces; 4.3. Construction; 4.4. Dual space; 4.5. Complements; 4.6. Coregular and conull; 4.7. The FK program; CHAPTER 5. REPLACEABILITY AND CONSISTENCY; 5.1. Functional analysis; 5.2. Replaceability; 5.3. Consistency; 5.4. Reversible matrices; 5.5. Row-finite and one to one; 5.6. Bounded consistency; CHAPTER 6. BIGNESS THEOREMS; 6.0. Functional analysis; 6.1. c not closed; 6.2. Two-norm convergence and W
• 6.3. Oscillation6.4. Conull spaces; 6.5. Coregular spaces and matrices; 6.6. Subspace of l a; 6.7. Bigness; CHAPTER 7. SEQUENCE SPACES; 7.0. Functional analysis; 7.1. Monotone norms; 7.2. Duals; 7.3. Nine spaces; 7.4. Determining sets; CHAPTER 8. INCLUSION AND MAPPING; 8.0. Functional analysis; TABLE; 8.1. Introduction; 8.2. Inclusion; 8.3. Mapping theorems; 8.4. Examples; 8.5. Mapping concluded; 8.6. Functional dual; CHAPTER 9. SEMICONSERVATIVE SPACES AND MATRICES; 9.1. Introduction; 9.2. Semiconservative spaces; 9.3. Coregular and conull; 9.4. Matrix domains; 9.5. Matrices
• 9.6. Coregular and conull matricesCHAPTER 10. DISTINGUISHED SUBSPACES OF FK SPACES; 10.0. Functional analysis; 10.1. Duals as BK spaces; 10.2. Distinguished subspaces; 10.3. The subspace B; 10.4. The subspace F; 10.5. The subspace W; 10.6. Basis; CHAPTER 11. EXTENSION; 11.0. Functional analysis; 11.1. Row functions; 11.2. Matrices; CHAPTER 12. DISTINGUISHED SUBSPACES OF MATRIX DOMAINS; 12.0. Functional analysis; 12.1. Matrix domains; 12.2. Associativity; 12.3. AK spaces; 12.4. Weak and strong convergence; 12.5. c-like spaces; CHAPTER 13. DISTINGUISHED SUBSPACES OF cA
• 13.1. B and the perfect part 20113.2. The inset and replaceability; 13.3. The main theorem; 13.4. Applications; 13.5. Almost coregular and very conull; CHAPTER 14. THE FUNCTIONAL μ; 14.0. Functional analysis; 14.1. Parts of the dual; 14.2. The functional μ; 14.3. The strong topology; 14.4. μ spaces; 14.5. AB and closure of Xß; CHAPTER 15. THE SUBSPACE P; 15.0. Functional analysis; 15.1. T and the test functions; 15.2. The subspace P; 15.3. Factorization; 15.4. Inclusion and invariance; 15.5. Replaceability; 15.6. Miscellany and questions; CHAPTER 16. SEQUENTIAL COMPLETENESS AND SEPARABILITY
• 16.0. Functional analysis
• Summability is an extremely fruitful area for the application of functional analysis; this volume could be used as a source for such applications. Those parts of summability which only have ``hard'' (classical) proofs are omitted; the theorems given all have ``soft'' (functional analytic) proofs.
• English