1st Edition

Summable Spaces and Their Duals, Matrix Transformations and Geometric Properties

By Feyzi Başar, Hemen Dutta Copyright 2020
    172 Pages 20 B/W Illustrations
    by Chapman & Hall

    172 Pages 20 B/W Illustrations
    by Chapman & Hall

    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.


    • 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


    1. Linear Sequence Spaces and Matrix Domains in Sequence Spaces. 2. Some Normed Sequence Spaces Generated by Certain Triangles. 3. Some Paranormed Spaces Derived by the Double Sequential Band Matrix. 4. Paranormed Nörlund Sequence Spaces. 5. Generalized Orlicz Sequence Spaces.


    Dr. Feyzi Başar is a Professor Emeritus since July 2016, at İnönü University, Turkey. He has published an e-book for graduate students and researchers and more than 150 scientific papers in the field of summability theory, sequence spaces, FK-spaces, Schauder bases, dual spaces, matrix transformations, spectrum of certain linear operators represented by a triangle matrix over some sequence space, the alpha-, beta- and gamma-duals and some topological properties of the domains of some double and four dimensional triangles in certain spaces of single and double sequences, sets of the sequences of fuzzy numbers, multiplicative calculus. He has guided 17 master and 10 Ph.D. students, served as a referee for 121 international scientific journals. He is the member of editorial board of 21 scientific journals. He is also a member of scientific committee of 17 mathematics conferences, delivered talks at 14 different universities as invited speaker and participated in more than 70 mathematics symposiums with papers.

    Dr. Hemen Dutta has been rendering his service as teaching faculty member in mathematics at Gauhati University, India. His research areas include functional analysis, mathematical modelling, etc. He has to credit over 100 items as research papers and book chapters, and also 10 books so far. He has acted as resource person in different academic events, and delivered invited talks at national and international levels. He has visited several foreign countries on invitations for research collaboration and delivering talks. He has conducted 5 academic events so far and associated with several conferences in different capacities. He is also involved with publishing thematic issues in journals and book series. He is actively involved in popularizing mathematics education in different ways from school to higher levels. He was honorary joint secretary of the Assam Academy of Mathematics for two years during 2014-2015. He is also a life member of several mathematical societies. He has authored articles for newspaper, scientific magazines, science portals, popular books, etc.