EMIS ELibM Electronic Journals Publications de l'Institut Mathématique, Nouvelle Série
Vol. 90(105), pp. 135–143 (2011)

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Neeraj Srivastava, S. Bhattacharya, S. N. Lal

National Academy for Scientific Development, Education and Research "Shashi Villa", Banaras Hindu University, Varanasi, India; Department of Mathematics, Faculty of Science, Banaras Hindu University, Varanasi, India

Abstract: In \cite{Srivastava}, we have given a new definition of real or complex 2-normed algebras and 2-Banach algebras. Here we give two examples which establish that not all 2-normed algebras are normable and a 2-Banach algebra need not be a 2-Banach space. We conclude by deriving a new and interesting spectral radius formula for 1-Banach algebras from the basic properties of 2-Banach algebras and thus vindicating our definitions of 2-normed and 2-Banach algebras given in \cite{Srivastava}.

Classification (MSC2000): 46A, 46H

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Electronic fulltext finalized on: 16 Nov 2011. This page was last modified: 30 Nov 2011.

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