Titlebook: An Introduction to Ultrametric Summability Theory; P.N. Natarajan Book 2015Latest edition The Editor(s) (if applicable) and The Author(s),

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Ultrametric Functional Analysis,ic set up too. However, the Hahn–Banach theorem fails to hold. To salvage the Hahn–Banach theorem, the concept of a “spherically complete field” is introduced and Ingleton’s version of the Hahn–Banach theorem is proved. The classical “convexity” does not work in the ultrametric set up and it is repl

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Ultrametric Summability Theory,n the topic) to the present. In the present chapter, Silverman–Toeplitz theorem is proved using the “sliding-hump method”. Schur’s theorem and Steinhaus theorem also find a mention. Core of a sequence and Knopp’s core theorem is discussed. It is proved that certain Steinhaus-type theorems fail to hold.

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https://doi.org/10.1007/978-81-322-2559-1Archimedean axiom; Canonical expansion; Double sequences; Hahn-Banach theorem; Schur‘s theorem; The Nörlu

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