Several different notions of {\em bounded} element of a topological *-algebra $\A$ are considered. The case where boundedness is defined via the natural order of $\A$ is examined in more details and it is proved that under certain circumstances (in particular, when $\A$ possesses sufficiently many *-representations) {\em order boundedness} is equivalent to {\em spectral boundedness}.
title = "Order bounded elements of topological *-algebras",
abstract = "Several different notions of {\em bounded} element of a topological *-algebra $\A$ are considered. The case where boundedness is defined via the natural order of $\A$ is examined in more details and it is proved that under certain circumstances (in particular, when $\A$ possesses sufficiently many *-representations) {\em order boundedness} is equivalent to {\em spectral boundedness}.",
T1 - Order bounded elements of topological *-algebras
AU - Trapani, Camillo
PY - 2012
Y1 - 2012
N2 - Several different notions of {\em bounded} element of a topological *-algebra $\A$ are considered. The case where boundedness is defined via the natural order of $\A$ is examined in more details and it is proved that under certain circumstances (in particular, when $\A$ possesses sufficiently many *-representations) {\em order boundedness} is equivalent to {\em spectral boundedness}.
AB - Several different notions of {\em bounded} element of a topological *-algebra $\A$ are considered. The case where boundedness is defined via the natural order of $\A$ is examined in more details and it is proved that under certain circumstances (in particular, when $\A$ possesses sufficiently many *-representations) {\em order boundedness} is equivalent to {\em spectral boundedness}.