Order Bounded Elements of Topological *-algebras

Abstract

Several different notions of bounded element of a topological *-algebra $\mathfrak{A}$ are considered. The case where boundedness is defined via the natural order of $\mathfrak{A}$ is examined in more details and it is proved that under certain circumstances (in particular, when $\mathfrak{A}$ possesses sufficiently many *-representations) order boundedness is equivalent to spectral boundedness