Abstract

In this paper, we introduce the notion of \emph{almost $n$-multiplier} on Banach algebras. This new notion generalizes the concept of $n$-multiplier introduced and studied in [J. Laali, M. Fozouni, \emph{$n$-multipliers and their relations with $n$-homomorphisms}, Vietnam J. Math., \textbf{45} (2017), 451-457]. We gave some general results and the continuity of such maps with some examples for this new notion on Banach algebras. In particular, we generalize the celebrated theorem of Johnson to (left) $n$-multipliers on Banach algebras.

Keywords: Almost $n$-multiplier; automatic continuity; uniform Banach algebra.

MSC: 46H40, 47B48, 47A10

DOI: 10.57016/MV-SCI80S02

Pages:  1--9