Banach-Alaoglu theorem for Hilbert $H^{\ast }$-module

Abstract

We provided an analogue Banach-Alaoglu theorem for Hilbert $H^{\ast }$-module. We construct a $\Lambda$-weak${}^{\ast }$ topology on a Hilbert $H^{\ast }$-module over a proper $H^{\ast }$-algebra $\Lambda$, such that the unit ball is compact with respect to $\Lambda$-weak${}^{\ast }$ topology.