**Best Reference Books on Sequence Spaces**, which are used by students of top universities, and colleges. This will help you choose the right book depending on if you are a beginner or an expert. Here is the complete list of

**Sequence Spaces Books**with their authors, publishers, and an unbiased review of them as well as links to the Amazon website to directly purchase them. If permissible, you can also download the free PDF books on Sequence Spaces below.

1."Sequence Spaces and Measures of Noncompactness with Applications to Differential and Integral Equations" by Józef Banaś and Mohammad Mursaleen
“Sequence Spaces and Measures of Noncompactness with Applications to Differential and Integral Equations” Book Review: This book talks about a special idea called “measures of noncompactness” and how they can be used to solve different types of math problems. It has eight parts that explain things like sequence spaces, matrix transformations, and measures of noncompactness. The book also talks about how these ideas can be used to solve problems related to differential and integral equations. The book has examples that can help students understand the ideas and it’s good for people who want to learn more about this topic.
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2."Sequence Spaces and Applications" by Eberhard Malkowsky and P K Jain
“Sequence Spaces and Applications” Book Review: This book is about new ways to understand how things work in math, called functional analysis and operator theory. It talks about solving many problems with a lot of numbers by using some special ways to simplify things. The authors explain everything in detail so that even people who are not experts can understand it. The book is for people who have studied math a lot already and want to learn more. It covers three big topics: Classical Sequence Spaces, Duals and Matrix Transformation, and Structure and Topology.
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3."Sequence Spaces and Nonarchimedean Analysis" by Sudarsan Nanda
“Sequence Spaces and Nonarchimedean Analysis” Book Review: This book explains new advancements in sequence spaces, matrix transformations, and non-archimedean analysis. The book discusses topics such as convergence, duality, Banach limits, matrix transformations, Banach spaces, Banach algebras and more. Even though the book begins with basic ideas, many of the results presented here have never been published before. This book is not only for students but also for researchers who want to refer to this information.
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4."Infinite Matrices and Compact Operators on Sequence Spaces" by Abdullah K Noman
“Infinite Matrices and Compact Operators on Sequence Spaces” Book Review: This book is about matrix operators on a type of sequence space called ℓp(r,s,t;B(m))ℓp(r,s,t;B(m)), which is related to ℓpℓp spaces. The book discusses how to calculate the operator norms and the Hausdorff measures of noncompactness of these matrix operators. It also talks about how to use the Hausdorff measure of noncompactness to determine if these operators are compact. In addition, the book explores the properties of this space and introduces some new sequence spaces. This book is useful for researchers who want to study these topics in detail.
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5."Double Sequence Spaces and the Difference Operator" by Bipul Sarma
“Double Sequence Spaces and the Difference Operator” Book Review: This book is about double sequences, which are like single sequences but are infinite matrices. The book talks about different types of linear spaces of double sequences and their properties. The difference operator is used on double sequences to make a new one. Depending on how the sequences behave, different sequence spaces are created and studied using functional analysis. This book is for people interested in analysis, linear algebra, and functional analysis. The study of double sequence spaces is new in functional analysis, and the book includes some new results. The first chapter covers the basics of double sequences and difference operators, and the last two chapters include new ideas and results.
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6."Statistical and Lacunary Statistical Convergence of Sequence Spaces" by Anindita Basu
“Statistical and Lacunary Statistical Convergence of Sequence Spaces” Book Review: This book is about sequence spaces and new convergence methods like statistical convergence, lacunary convergence, and lacunary statistical convergence. The author of this book developed new classes of statistical and lacunary convergent sequences using Orlicz and Modulus functions. They also introduced these convergence methods in the space of vector-valued double difference sequences. They extended the concept of statistical convergence to composite vector-valued sequence spaces and proved some results similar to those obtained by earlier authors. They combined matrix summability, lacunary convergence, Orlicz functions, and difference sequences to obtain a new class of sequence spaces that generalizes many known sequence spaces and is important for comparison to vector-valued strongly Cesaro-type summable sequence spaces.
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7."Ideal Convergent Sequence Spaces on Linear Operators" by A Khan Vakeel and Shafiq Mohd
“Ideal Convergent Sequence Spaces on Linear Operators” Book Review: The goal of this book is to provide conditions for a sequence space defined in Lim to be considered as an operator ideal, where all bounded linear operators between Banach spaces have bounded nth approximation numbers. The book focuses on studying different sequence spaces, especially those that converge under statistical and I-convergence, with the intention of helping students and researchers working in this field. The book introduces I-convergent sequence spaces and analyzes their properties, including algebraic and topological properties, inclusion relations, decomposition theorems, and other related results.
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8."Matrix Operators Involving Sequence Spaces" by Rao K Chandrasekhara
“Matrix Operators Involving Sequence Spaces” Book Review: This book talks about different sequence spaces like l_infinity, C, and c_not, as well as Space l, Space of Entire sequences, Special Methods, Cesaro Spaces, and Rate spaces. It is written for researchers who study Functional Analysis, Summability Theory, and Mathematical Analysis. The theory of sequence spaces is a part of Functional Analysis. The book covers current topics in sequence spaces.
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9."Double Sequence Spaces and Orlicz Functions" by Vakeel A Khan and Sabiha Tabassum
“Double Sequence Spaces and Orlicz Functions” Book Review: This book talks about some types of sequences that are both entire and analytic, and it uses Orlicz functions to define them. This book is helpful for people who are studying or planning to study sequence space theory. The main goal of the book is to explore new types of sequence spaces defined by Orlicz Functions. The book also discusses problems related to these sequence spaces in 2-normed and n-normed spaces. It also looks at some important properties related to algebra and topology, and examines how these classes of sequences are related to each other.
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10."Infinite Matrices and Sequence Spaces (Dover Books on Mathematics)" by Richard Cooke
“Infinite Matrices and Sequence Spaces (Dover Books on Mathematics)” Book Review: This book explains important information about infinite matrices in a clear and accurate way. It focuses on how infinite matrices behave in general, not just on specific types of matrices. The first three chapters of the book teach readers how to work with infinite matrices by covering important definitions and concepts. They also talk about how to solve linear equations with infinite matrices and find the reciprocal of an infinite matrix. From chapter four onwards, the author discusses how infinite matrices can be used to solve problems related to sequences and series that don’t converge. Topics covered in these chapters include consistency, mutual consistency, and absolute equivalence; the core of a sequence; inefficiency and efficiency problems; Hilbert vector space and Hilbert matrices; and projective and distance convergence and limit in sequence spaces. Each chapter has examples to help readers understand the concepts better.
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