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International Journal of Modern Computation, Information and Communication Technology

ISSN 2581-5954

October 2018, Vol. 1, Issue 5, p. 99-102.​​

On Characterization of Very Rotund Banach Spaces   
A. O. Wanjara, N. B. Okelo*, O. Ongati
Department of Pure and Applied Mathematics, Jaramogi Oginga Odinga University of Science and Technology, P.O. Box 210-40601, Bondo-Kenya.
*Corresponding author’s e-mail:
bnyaare@yahoo.com     

Abstract

It is known that the Hilbert space H is the most rotund space among all Banach spaces. The question whether if a normed space X is a rotund Banach space implies we can obtain other most rotund spaces is still open and represents one of the most interesting and studied problems. In this paper we investigate if there exists other most rotund Banach spaces. It is shown that Frechet spaces are very rotund and also uniformly rotund.

Keywords: Rotundity; Hilbert space; Modulus; Convexity; Frechet space.

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