A certain class of pro C*- algebras and bounded elements of a Hilbert module

M. Kardel, R. G. Sanati

In this paper, introducing the notion of topologically simple pro C*-algebras, we show that direct product of C*-algebras K(Hi), as the set of all compact operators on a Hilbert space Hi, is a topologically simple pro C*-algebra. Applying this fact, we prove that the set of all bounded elements of a certain class of Hilbert modules are dense in the same module. 

Tbilisi Mathematical Journal, Vol. 14(2) (2021), pp. 59-64