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

Chapter

Abstract

In this chapter, we define the core of a sequence and prove an improvement of Sherbakhoff’s result, which gives rise to a short and elegant proof of Knopp’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 

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Copyright information

© Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  1. 1.Formerly of the Department of MathematicsRamakrishna Mission Vivekananda CollegeChennaiIndia

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