Core of a Sequence and the Matrix Class $$(\ell, \ell )$$

P. N. Natarajan ()
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P. N. Natarajan: Ramakrishna Mission Vivekananda College, Formerly of the Department of Mathematics

Chapter Chapter 2 in Classical Summability Theory, 2017, pp 27-36 from Springer

Abstract: Abstract In this chapter, weCore of a sequence define the core of a sequence and prove an improvement of Sherbakhoff’sSherbakhoff result, which gives rise to a short and elegant proof of Knopp’s core theoremKnopp’s core theorem . We also present some nice properties of the class $$(\ell , \ell )$$ of infinite matrices.

Keywords: Core of a sequence; Generalized $$\alpha $$ -core; Sherbakhoff’s theorem; Knopp’s core theorem; The matrix class $$(\ell; \ell )$$; Banach algebra; Closed; Convex; Semigroup; Convolution product; Mercerian theorem (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-10-4205-8_2

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DOI: 10.1007/978-981-10-4205-8_2

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