دانلود کتاب Sequence Spaces and Summability over Valued Fields

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Cover Half Title Title Page Copyright Page Dedication Contents About the Author Foreword Preface 1. Preliminaries 1.1 Valuation and the topology induced by it 1.2 Kinds of valuations 1.3 Normed linear spaces 1.4 K-convexity and locally K-convex spaces 1.5 Topological algebras 1.6 Summability methods 2. On Certain Spaces Containing the Space of Cauchy Sequences 2.1 Introduction 2.2 Summability of sequences of 0's and 1's 2.3 Some structural properties of ℓ∞ 2.4 The Steinhaus theorem 2.5 A Steinhaus-type theorem 3. Matrix Transformations between Some Other Sequence Spaces 3.1 Introduction 3.2 Characterization of matrices in (ℓα,ℓα), α>0 3.3 Multiplication of series 3.4 A Mercerian theorem 3.5 Another Steinhaus-type theorem 3.6 Characterization of matrices in (ℓ(p),ℓ∞) 4. Characterization of Regular and Schur Matrices 4.1 Introduction 4.2 Summability of subsequences and rearrangements 4.3 The core of a sequence 5. A Study of the Sequence Space c0(p) 5.1 Identity of weak and strong convergence or the Schur property 5.2 Normability 5.3 Nuclearity of c0(p) 5.4 c0(p) as a Schwartz space 5.5 c0(p) as a metric linear algebra 5.6 Step spaces 5.7 Some more properties of the sequence space c0(p) 6. On the Sequence Spaces ℓ(p), c0(p), c(p), ℓ∞(p) over Non-Archimedean Fields 6.1 Introduction 6.2 Continuous duals and the related matrix transformations 6.3 Some more properties of the sequence spaces ℓ(p),c0(p) and ℓ∞(p) 6.4 On the algebras (c,c) and (ℓα,ℓα) 7. A Characterization of the Matrix Class (ℓ∞,c0) and Summa-bility Matrices of Type M in Non-Archimedean Analysis 7.1 Introduction 7.2 A Steinhaus-type theorem 7.3 A characterization of the matrix class (ℓ∞,c0) 7.4 Summability matrices of type M 8. More Steinhaus-Type Theorems over Valued Fields 8.1 Introduction 8.2 A Steinhaus-type theorem when K = R or C 8.3 Some Steinhaus-type theorems over valued elds 8.4 Some more Steinhaus-type theorems over valued fields I 8.5 Some more Steinhaus-type theorems over valued fields II Index