Banach-Alaoglu theorem for Hilbert $H^*$-module

Abstract

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