Banach Limit and Applications 1st Edition by Gokulananda Das, Sudarsan Nanda ISBN 9780367698652 036769865X

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Product details:

ISBN 10: 036769865X
ISBN 13: 9780367698652
Author: Gokulananda Das, Sudarsan Nanda

Banach Limit and Applications 1st Edition Table of contents:

1 Introduction

2 Hahn-Banach Theorem and Generalizations

2.1 Extended form of Hahn-Banach Theorem

2.1.1 Discussion

2.2 Invariant linear functionals

2.3 Hahn-Banach Theorem for semifields

2.4 Sandwich version of Hahn-Banach Theorem

2.5 Hahn-Banach Theorem for modules

3 Banach and Generalized Limits

3.1 Banach limits

3.2 Sublinear functionals generating Banach limits

3.3 Sublinear functional that dominates all Banach limits

3.4 Sublinear functionals involving regular matrices

3.5 Invariant limits

3.6 Generalizations of Banach limit

3.7 Invariant means

3.8 Further generalization

4 Almost Convergence

4.1 Unique Banach limits

4.2 Properties and examples of almost convergent sequences

4.2.1 Examples of almost convergent sequences

4.2.2 Periodic sequence

4.3 Almost convergence and matrix method

4.4 Almost convergence and uniform distribution of sequences.

4.4.1 Three parameter matrices

4.5 Well-distributed sequences

4.6 Almost convergence and statistical convergence

4.6.1 Properties

4.7 Almost convergence, density, and uniform density

4.8 Almost convergence and uniform law of large numbers

4.9 Almost convergence and almost ergodicity

5 Core Theorems

5.1 Knopp’s Core

5.2 Banach Core

5.3 Generalized CORE theorems

5.4 Main theorems

6 Absolute Almost Convergence

6.1 Introducing the new sequence space

6.2 Emerging eight spaces

6.3 Theorems

6.4 Application of absolute almost convergence to Fourier series

6.5 Tauberian Theorem

7 The Space î(P)

7.1 New sequence spaces î(P) and î^

7.1.1 An important property

7.2 Some topological properties

7.3 Some further properties

7.4 Some further topological properties

7.5 Some outstanding conjectures

7.6 Absolute Banach limits

8 Strong Almost Convergence

8.1 Strong almost convergence

8.2 Strong σ – almost convergence

8.3 On lacunary strong almost convergence

9 Functional Banach Limits

9.1 Preliminaries

9.2 Functional Banach limits

9.3 The sets Sα and |Sα|

9.4 Absolute almost convergence

9.5 Strong almost convergence

10 Matrix Transformations

10.1 Introduction

10.2 The classes (l∞(p), ĉ) and (c(p)ĉ)

10.3 The classes (l(p), ĉ)

10.4 The spaces ĉ0(p) and ĉ(p)

10.5 The classes (v, ĉ)

10.6 The class (ĉ, c)

10.7 The class (l1, lp)

10.8 The class (l∞, lp)

10.9 The class (lp, lp)

10.10 Some open problems

11 Absolutely Almost and Strongly Almost Summable Sequences

11.1 Introduction

11.2 Absolute almost summability

11.3 Strong almost summability

11.4 Strong almost (Z, k) summability

11.5 Spaces of strongly almost summable sequences

Bibliography

Index

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Tags: Gokulananda Das, Sudarsan Nanda, Banach Limit, Applications