Malaysian Journal of Mathematical Sciences, June 2026, Vol. 20, No. 2
On Bounded \(m-\)Linear Operators in 2-Normed Spaces
Meitei, S. R., Singh, M. P.
Corresponding Email: romenmoirang@gmail.com
Received date: 15 February 2025
Accepted date: 31 October 2025
Abstract:
The abstraction of bounded \(m-\)linear operators in normed spaces is extended in a new direction. Three statements on continuity of the operators are proved to be identical, and the space of operators \(\mathcal{B}(W^m, V ), \|.\|)\) is shown to be Banach if \((V,\|.\|)\) is Banach. Moreover, the definition of bounded \(m-\)linear operators in normed spaces is generalized to 2-normed spaces and accordingly, we extend related propositions and theorems.
Keywords: Banach space; 2-normed space; \(m-\)normed space; \(m-\)linear operator; continuity.
