Functional Analysis and Summability [#1017517]

P.N. Natarajan, "Functional Analysis and Summability"
English | ISBN: 0367544490 | 2020 | 240 pages | MOBI | 3 MB
There are excellent books on both 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 students. In the functional analysis component of the book, the Hahn-Banach theorem, Banach-Steinhaus theorem (or uniform boundedness principle), the open mapping theorem, the closed graph theorem, and the Riesz representation theorem are highlighted. In the summability component of the book, the Silverman-Toeplitz theorem, Schur's theorem, the Steinhaus theorem, and the Steinhaus-type theorems are proved. The utility of functional analytic tools like the uniform boundedness principle to prove some results in summability theory is also pointed out.