2-normed algebras-II

Abstract

In the first part of the paper [5], we gave 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 [5].

Inconveniences and Mobility Issues of Elders on Road: The Case of Kolkata Municipal Corporation, West Bengal, India

“…Thus, X is a n-Banach algebra with the indentity ( θ, 1 ). For 2-normed algebra augmentation of unity is discussed by N. Srivastava et al [15].…”

“…Mohammed and Siddiqui [11] introduced the concept of 2-Banach algebra and derived analog of some known results of the usual Banach algebra in 2-Banach algebra. For more on 2-normed algebras on can go through the papers [15,16].…”