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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}.

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}.