Summable Spaces and Their Duals, Matrix Transformations and Geometric Properties (Chapman & Hall/CRC Monographs and Research Notes in Mathematics)

✍ Scribed by Feyzi Başar, Hemen Dutta

• Publisher: Chapman and Hall/CRC
• Year: 2020
• Tongue: English
• Leaves: 173
• Edition: 1
• Category: Library

✦ Synopsis

The aim of Summable Spaces and Their Duals, Matrix Transformations and Geometric Properties is to discuss primarily about different kinds of summable spaces, compute their duals and then characterize several matrix classes transforming one summable space into other. The book also discusses several geometric properties of summable spaces, as well as dealing with the construction of summable spaces using Orlicz functions, and explores several structural properties of such spaces.

Each chapter contains a conclusion section highlighting the importance of results, and points the reader in the direction of possible new ideas for further study.

Features

• Suitable for graduate schools, graduate students, researchers and faculty, and could be used as a key text for special Analysis seminars
• Investigates different types of summable spaces and computes their duals
• Characterizes several matrix classes transforming one summable space into other
• Discusses several geometric properties of summable spaces
• Examines several possible generalizations of Orlicz sequence spaces

✦ Table of Contents

Cover
Half Title
Series Page
Title Page
Copyright Page
Dedication
Contents
Preface
Authors
List of Abbreviations and Symbols
1. Linear Sequence Spaces and Matrix Domains in Sequence Spaces
1.1 Linear Sequence Spaces
1.1.1 Metric Sequence Spaces
1.1.2 The Space ω
1.1.3 The Space ℓ∞
1.1.4 The Spaces f and f0
1.1.5 The Spaces c and c0
1.1.6 The Space ℓp
1.1.7 The Space bs
1.1.8 The Spaces cs and cs0
1.1.9 The Spaces bv and bv1
1.1.10 The Spaces ωp0, ωp and ωp∞
1.1.11 Normed Sequence Spaces
1.1.12 The Dual Spaces of a Sequence Space
1.1.13 Paranormed Sequence Spaces
1.1.14 The Spaces ℓ∞(p), c(p) and c0(p)
1.1.15 The Space ℓ(p)
1.1.16 The Spaces ω∞(p), ω(p) and ω0(p)
1.1.17 The Paranormed Space of Almost Convergent Sequences
1.1.18 The Spaces bs(p), cs(p) and cs0(p)
1.2 Matrix Domains in Sequence Spaces
1.2.1 Preliminaries, Background and Notations
2. Some Normed Sequence Spaces Generated by Certain Triangles
2.1 Normed Nörlund Sequence Spaces
2.1.1 The Sequence Spaces c0(Nt) and c(Nt) of Non-absolute Type
2.1.2 The Alpha-, Beta- and Gamma-duals of the Spaces c0(Nt) and c(Nt)
2.1.3 Matrix Transformations Related to the Sequence Space c(Nt)
2.1.4 The Spaces of Nörlund Almost Null and Nörlund Almost Convergent Sequences
2.1.5 The Alpha-, Beta- and Gamma-duals of the Spaces f0(Nt) and f(Nt)
2.1.6 Matrix Transformations Related to the Space f(Nt)
2.2 Domains of the Euler-Cesàro Difference Matrix in the Classical Sequence Spaces
2.2.1 The Euler-Cesàro Difference Spaces of Null, Convergent and Bounded Sequences
2.2.2 The Alpha-, Beta- and Gamma-duals of the Spaces ℓ∞, c and c0
2.2.3 Matrix Transformations Related to the Sequence Space c
2.2.4 The Euler-Cesàro Difference Spaces of Absolutely p-Summable Sequences
2.2.5 The Alpha-, Beta- and Gamma-duals of the Space ℓp
2.2.6 Matrix Transformations on the Sequence Space ℓp
2.3 Spaces of Fibonacci Difference Sequences
2.3.1 The Fibonacci Difference Spaces of Absolutely p-Summable, Null and Convergent Sequences
2.3.2 The Alpha-, Beta- and Gamma-duals of the Spaces ℓp(F), c0(F) and c(F), and Some Matrix Transformations
2.4 Conclusion
3. Some Paranormed Spaces Derived by the Double Sequential Band Matrix
3.1 Domains of the Double Sequential Band Matrix in Some Maddox's Spaces
3.1.1 The Spaces ℓ∞(B,p), c(B,p) and c0(B,p), and Their Topological Properties
3.1.2 Alpha-, Beta- and Gamma-duals of the Spaces ℓ∞(B,p), c(B,p) and c0(B,p)
3.1.3 Matrix Transformations
3.2 The Sequence Space ℓ(B,p) of Non-absolute Type
3.2.1 The Alpha-, Beta- and Gamma-duals of the Space ℓ(B,p)
3.2.2 Matrix Transformations on the Sequence Space ℓ(B,p)
3.2.3 The Rotundity of the Space ℓ(B,p)
3.3 Conclusion
4. Paranormed Nörlund Sequence Spaces
4.1 Paranormed Nörlund Sequence Spaces
4.1.1 The Nörlund Sequence Space Nt(p)
4.1.2 The Alpha-, Beta- and Gamma-duals of the Space Nt(p)
4.1.3 Some Matrix Transformations Related to the Sequence Space Nt(p)
4.1.4 The Rotundity of the Space Nt(p)
4.2 Conclusion
5. Generalized Orlicz Sequence Spaces
5.1 Orlicz Sequence Spaces
5.2 Orlicz Sequence Spaces Generated by Difference Operator
5.3 Orlicz Sequence Spaces Generated by Cesàro Mean
5.4 Generalized Modular Sequence Spaces
5.5 Conclusion
Bibliography
Index