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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Sherbakoff, A.A.: On cores of complex sequences and their regular transform. Mat. Zametki 22, 815–828 (1977) (Russian)
Natarajan, P.N.: On the core of a sequence over valued fields. J. Indian. Math. Soc. 55, 189–198 (1990)
Cooke, R.G.: Infinite Matrices and Sequence Spaces. Macmillan, New York (1950)
Fridy, J.A.: A note on absolute summability. Proc. Amer. Math. Soc. 20, 285–286 (1969)
Knopp, K., Lorentz, G.G.: Beiträge zur absoluten Limitierung. Arch. Math. 2, 10–16 (1949)
Maddox, I.J.: Elements of Functional Analysis. Cambridge University Press, Cambridge (1977)
Natarajan, P.N.: On the algebra \((\ell _1, \ell _1)\) of infinite matrices. Analysis (München) 20, 353–357 (2000)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2017 Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Natarajan, P.N. (2017). Core of a Sequence and the Matrix Class \((\ell , \ell )\) . In: Classical Summability Theory. Springer, Singapore. https://doi.org/10.1007/978-981-10-4205-8_2
Download citation
DOI: https://doi.org/10.1007/978-981-10-4205-8_2
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-4204-1
Online ISBN: 978-981-10-4205-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)