Multiplication is an open bilinear mapping in the Banach algebra of functions of bounded Wiener $p$-variation

Abstract

Let $BV_p[0,1], 1 \le p \lt \infty$, be the Banach algebra of functions of bounded $p$-variation in the sense of Wiener. Recently, Kowalczyk and Turowska [9] proved that the multiplication in $BV_1[0,1]$ is an open bilinear mapping. We extend this result for all values of $p \in [1,\infty)$.