Double Sequence Spaces and Four-Dimensional Matrices

Cover
Half Title
Title Page
Copyright Page
Dedication
Contents
Foreword
Preface
Authors
List of Abbreviations and Symbols
1. Spaces of Double Sequences and Series
	1.1. Double Sequence Spaces
	1.2. Double Series Spaces
	1.3. Four-Dimensional Infinite Matrices
	1.4. Some Topological Properties of the Spaces Almost Null and Almost Convergent Double Sequences
	1.5. Riesz Summability of Double Series
	1.6. Abel Summability of Double Series
	1.7. Conclusion
	1.8. Exercises
2. Some Paranormed Double Sequence Spaces
	2.1. Preliminaries, Background and Notations
	2.2. The Double Sequence Spaces Cp(t) and Cbp(t)
	2.3. Paranormed Space Mu(t) of Double Sequences
	2.4. Double Sequence Spaces Cp0(t), Cbp0(t) and Lu(t)
	2.5. Paranormed Spaces Cr(t), Cr0(t), Ctr(t) and Ctr0(t)
	2.6. Conclusion
	2.7. Exercises
3. Matrix Domain in Double Sequence Spaces
	3.1. Preliminaries, Background and Notations
	3.2. Certain Paranormed Difference Spaces of Double Sequences
	3.3. Double Sequence Spaces BS, BS(t), CS# and BV
	3.4. Difference Spaces of Almost Convergent and Strongly Almost Convergent Double Sequences
	3.5. Absolutely s-Summable Double Sequences
	3.6. Riesz Domains in Some Double Sequence Spaces
	3.7. Domain of Euler Mean in the Space of Absolutely s-summable Double Sequences With 0 < s < 1
	3.8. Conclusion
	3.9. Exercises
4. Dual Spaces of Double Sequence Spaces
	4.1. Preliminaries, Background and Notations
	4.2. Dual Spaces of Double Series
	4.3. Dual Spaces of Mu(t)
	4.4. Dual Spaces of Cp0(t), Cbp(t) and Cbp0(t)
	4.5. Dual Spaces of the Space Lu(t)
	4.6. The Alpha-dual of the Space Mu(t)
	4.7. Dual Spaces of the Spaces Cf(Δ), Cf0(Δ) and ...
	4.8. Dual Spaces of the Spaces Cr(t), Cr0(t), Ctr(t) and Ctr0(t)
	4.9. Dual Spaces of the Spaces BVs and LSs
	4.10. Dual Spaces of Riesz Spaces Rqt(Mu), Rqt(C#) and Rqt(Ls)
	4.11. Dual Spaces of Epsr Spaces
	4.12. Conclusion
	4.13. Exercises
5. Matrix Transformations Between Double Sequence Spaces
	5.1. Preliminaries, Background and Notations
	5.2. Characterizations of Some Matrix Classes
	5.3. Mercerian and Steinhaus Type Theorems for Four-Dimensional Matrices
	5.4. Comparison of Four-Dimensional Summability Methods
	5.5. Four-Dimensional Usual Dual Summability Methods
	5.6. Four-Dimensional Dual Summability Methods of the New Sort
	5.7. Summability of Unbounded Double Sequences
	5.8. Some Tauberian Theorems for Four-Dimensional Euler and Borel Summabilities
	5.9. Conclusion
	5.10. Exercises
Bibliography
Index