Bulletin of the
Korean Mathematical Society BKMS

The main purpose of this paper is to give the Wintner theorem in unital complete random normed algebras which is a random generalization of the classical Wintner theorem in Banach algebras. As an application of the Wintner theorem in unital complete random normed algebras, we also obtain that the identity operator on a complete random normed module is not a commutator.

Keywords: random normed module, random normed algebra, random spectrum, Wintner theorem

MSC numbers: 46H25, 46H05, 15A78