2-NORMED ALGEBRAS-II


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




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}.