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International Journal of Modern Computation, Information and Communication Technology

ISSN 2581-5954

March-April 2021, Vol. 4, Issue 3-4, p. 13-17.​​

On Isometrically Equivalent Norms in Banach Spaces
P. W.  Mulongo¹, S. Aywa¹, N. B. Okelo²*
¹Department of Mathematics, Kibabii University, Kenya.

²Department 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

Many studies on equivalent norms are playing an increasingly important role in the theory of Banach spaces. Also in consideration has been the characterization of operator ideals. In this paper we develop isometrically equivalent norms in a Banach space. The objectives of the study are to show that there exists Banach spaces which are isometrically isomorphic; develop an unconditional basis in a Banach space and renorm an equivalent norm under which a Banach space will become a Banach lattice and still remain a banach space. Authors showed that there exists Banach spaces which are isometric and isomorphic. Authors further showed that for a normal Banach space which is absolutely continuous, then there exists an unconditional basis in a Banach space.

Keywords: Banach space; Banach lattice; Unconditional basis; Isomorphic.

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