Kindly note that we have put a lot of effort into researching the best books on Sequence Spaces subject and came out with a recommended list of top 10 best books. The table below contains the Name of these best books, their authors, publishers and an unbiased review of books on "Sequence Spaces" as well as links to the Amazon website to directly purchase these books. As an Amazon Associate, we earn from qualifying purchases, but this does not impact our reviews, comparisons, and listing of these top books; the table serves as a ready reckoner list of these best books.
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: Some of the existence results for various types of differential and integral equations by using measures of noncompactness are discussed in this book. This book deals with the study of sequence spaces, matrix transformations, measures of noncompactness and their various applications. The notion of measure of noncompactness is one of the most useful ones available and has many applications. The book consists of eight selfcontained chapters. Chapter 1 discusses the theory of FK spaces and Chapter 2 various duals of sequence spaces, which are used to characterize the matrix classes between these sequence spaces (FK and BK spaces) in Chapters 3 and 4. Chapter 5 studies the notion of a measure of noncompactness and its properties. The techniques associated with measures of noncompactness are applied to characterize the compact matrix operators in Chapters 6. In Chapters 7 and 8, some of the existence results are discussed for various types of differential and integral equations, which are obtained with the help of argumentations based on compactness conditions. Book provides suitable examples to help students understand the theory and also addresses researchers, as well as students, with an interest in getting acquainted with the topics.


2. “Sequence Spaces and Applications” by Eberhard Malkowsky and P K Jain
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“Sequence Spaces and Applications” Book Review: This book presents modern methods in functional analysis and operator theory along with their applications in recent research. The book also deals with the solvability of infinite systems of linear equations in various sequence spaces. It uses the classical sequence spaces, generalized Cesaro and difference operators to obtain calculations and simplifications of complicated spaces involving these operators. In order to make it selfcontained, comprehensive and of interest to a larger mathematical community, the authors have presented necessary concepts with results for advanced research topics. This book is intended for graduate and postgraduate students, teachers and researchers as a basis for further research, advanced lectures and seminars.The major topics covered are Classical Sequence Spaces, Duals and Matrix Transformation, Structure and Topology.


3. “Sequence Spaces and Nonarchimedean Analysis” by Sudarsan Nanda
“Sequence Spaces and Nonarchimedean Analysis” Book Review: This book presents the recent developments in the areas of sequence spaces, matrix transformations and non archimedean analysis. The topics covered include absolute and strong convergence, duality in sequence spaces, functional Banach limits, matrix transformations, valued fields, Banach spaces and Banach algebras over non archimedean fields. Although the book starts with basic concepts, most of the results presented here did not appear in any book before. Besides being used as a text for graduate students this book will be useful as a reference book for researchers working in this field.


4. “Infinite Matrices and Compact Operators on Sequence Spaces” by Abdullah K Noman
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“Infinite Matrices and Compact Operators on Sequence Spaces” Book Review: In this book, some identities or estimates for the operator norms and the Hausdorff measures of noncompactness of certain matrix operators on the sequence space ℓp(r,s,t;B(m))ℓp(r,s,t;B(m)) which is related to ℓpℓp spaces are derived. By applying the Hausdorff measure of noncompactness, we obtain the necessary and sufficient conditions for such operators to be compact. Further, we study some geometric properties of this space. The main aim of this book is to generalize some classical methods of summability, introduce some new sequence spaces and study their topological properties, duals and matrix transformations, and characterize some classes of compact operators on these spaces which can be obtained as an application of the Hausdorff measure of noncompactness.


5. “Double Sequence Spaces and the Difference Operator” by Bipul Sarma
“Double Sequence Spaces and the Difference Operator” Book Review: The generalized notion of single sequences are the double sequences. Every double sequence is an infinite matrix. various types of linear spaces of double sequences are constructed and studied their properties. The difference operator is used on the double sequences to construct a new double sequence. The double sequences may be bounded, unbounded, convergent, nonconvergent or some other. Depending on the behaviour of the sequences the sequence spaces are constructed and some properties of functional analysis are established. The book intends the role of infinite matrices to construct sequence spaces. Efforts have been done for the readers belonging to Analysis, Linear algebra and functional analysis. The studies on double sequence spaces are new in functional analysis. A few works have been done on the studies of different double sequence spaces. Hope that readers will be benefited for introducing new ideas from this book. A complete development on the studies of double sequences and difference operators is depicted in the first chapter of the book. In the remaining two chapters some new results are added.


6. “Statistical and Lacunary Statistical Convergence of Sequence Spaces” by Anindita Basu
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“Statistical and Lacunary Statistical Convergence of Sequence Spaces” Book Review: The development of the study of sequence spaces got momentum by the introduction of new convergence methods. Some of them are statistical convergence, lacunary convergence, lacunary statistical convergence etc.In the thesis, I have basically concentrated on various types of convergence methods and developed new classes of statistical and lacunary convergent sequences by using Orlicz and Modulus functions. We have also introduced these convergence methods in the space of vector valued double difference sequences. The concept of statistical convergence which is defined for locally convex topological vector space, seminormed space etc. has been extended for the class of composite vector valued sequence spaces and further, we have proved some results analogues to the results obtained by earlier authors. By combining the concepts of matrix summability, lacunary convergence, Orlicz functions, and difference sequences we obtained a new class of sequence spaces which generalizes many known sequence spaces and also plays an important role in comparison to vector valued strongly Cesarotype summable sequence spaces.


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 aim of this book is to give the sufficient conditions on the sequence space defined in Lim such that the class of all bounded linear operators between any arbitrary Banach spaces with nth approximation numbers of the bounded linear operators in form an operator ideal. This book is devoted to the study of some sequence spaces with the hope that it would be helpful to the students and researchers who want to work and study in the area of sequence spaces and its convergence under different names especially statistical and I convergence. In this book, the aim is to introduce some spaces of I – convergent sequences and study their algebraic and topological properties, inclusion relations, decomposition theorems and some other results on these spaces.


8. “Matrix Operators Involving Sequence Spaces” by Rao K Chandrasekhara
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“Matrix Operators Involving Sequence Spaces” Book Review: This book includes Sequence spaces l_infinity, C and c_not, Space l, Space of Entire sequences, Special Methods, Cesaro Spaces and Rate spaces. This monograph is meant for research – scholars who work in Functional Analysis, Summability Theory and Mathematical analysis. The theory of sequence spaces is a part of Functional analysis. Current topics in sequence spaces are discussed in this monograph.


9. “Double Sequence Spaces and Orlicz Functions” by Vakeel A Khan and Sabiha Tabassum
“Double Sequence Spaces and Orlicz Functions” Book Review: This book defines some classes of double entire and analytic sequences by means of Orlicz functions. This book will be very useful to postgraduates and for those who are doing research work or intend to work in the areas of classical and the modern sequence space theory. The main aim of this book is to study some new double sequence spaces defined by Orlicz Functions.We have also studied the problems of double sequence spaces in 2normed and nnormed spaces. Also studies some relevant algebraic and topological properties. Further some inclusion relations among the classes are also examined.


10. “Infinite Matrices and Sequence Spaces (Dover Books on Mathematics)” by Richard Cooke
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“Infinite Matrices and Sequence Spaces (Dover Books on Mathematics)” Book Review: This precise and accurate summation of basic results from a specialized field focuses on the behavior of infinite matrices in general, rather than on properties of special matrices. Three introductory chapters guide students to the manipulation of infinite matrices, covering definitions and preliminary ideas, reciprocals of infinite matrices, and linear equations involving infinite matrices. From the fourth chapter onward, the author treats the application of infinite matrices to the summability of divergent sequences and series from various points of view. Topics include consistency, mutual consistency, and absolute equivalence; the core of a sequence; the inefficiency and the efficiency problems for infinite matrices; Hilbert vector space and Hilbert matrices; and projective and distance convergence and limit in sequence spaces. Each chapter concludes with examples.


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