Functional Analysis and Summability
P.N. Natarajan, "Functional Analysis and Summability"
English | ISBN: 0367544490 | 2020 | 240 pages | AZW3 | 19 MB
English | ISBN: 0367544490 | 2020 | 240 pages | AZW3 | 19 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.
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