Ebook: Functional analysis and summability

Some basic concepts in functional analysis -- Linear transformations, linear functionals and convexity -- Hahn-Banach theorem -- Reflexivity -- Banach-Steinhaus theorem -- Closed graph theorem and open mapping theorem -- Hilbert spaces -- Silverman-Toeplitz theorem and Schur's theorem -- Steinhaus type theorem.;"There are excellent books on both the topics Functional Analysis and Summability. Most of them are very terse. In Functional Analysis and Summability, the author makes a sincere attempt for a gentle introduction of these topics to the students. In the Functional Analysis component of the book, Hahn-Banach theorem, Banach-Steinhaus theorem (or Uniform Boundedness Principle), Open mapping theorem, Closed graph theorem and Riesz representation theorem are highlighted. In the Summability component of the book, Silverman-Toeplitz theorem, Schur's theorem, Steinhaus theorem and Steinhaus type theorems are proved. The utility of functional analytic tools like Uniform Boundedness principle to prove some results in Summability Theory is also pointed out. Features: A sincere attempt made by the author for a soft and gentle introduction of the topics to the students; Basic results of Functional Analysis and Summability theory are highlighted; Applications of these results are also brought out; A lot of examples have been provided in the text wherever needed; Useful exercises are added at the end of each chapter. The book will be useful to post graduate students, pre research level students and research scholars in Mathematics. Students of Physics and Engineering will also find this book useful since topics in the book also have applications in related areas"--