TY - JOUR
T1 - Fully representable and *-semisimple topological partial *-algebras
AU - Trapani, Camillo
AU - Bellomonte, Giorgia
AU - Antoine, Jean-Pierre
PY - 2012
Y1 - 2012
N2 - We continue our study of topological partial *-algebras, focusingour attention to *-semisimple partial *-algebras, that is, those that possessa multiplication core and su ciently many *-representations. We discuss therespective roles of invariant positive sesquilinear (ips) forms and representablecontinuous linear functionals and focus on the case where the two notions arecompletely interchangeable (fully representable partial *-algebras) with thescope of characterizing a *-semisimple partial *-algebra. Finally we describevarious notions of bounded elements in such a partial *-algebra, in particular,those defined in terms of a positive cone (order bounded elements). The outcomeis that, for an appropriate order relation, one recovers the M-boundedelements introduced in previous works.
AB - We continue our study of topological partial *-algebras, focusingour attention to *-semisimple partial *-algebras, that is, those that possessa multiplication core and su ciently many *-representations. We discuss therespective roles of invariant positive sesquilinear (ips) forms and representablecontinuous linear functionals and focus on the case where the two notions arecompletely interchangeable (fully representable partial *-algebras) with thescope of characterizing a *-semisimple partial *-algebra. Finally we describevarious notions of bounded elements in such a partial *-algebra, in particular,those defined in terms of a positive cone (order bounded elements). The outcomeis that, for an appropriate order relation, one recovers the M-boundedelements introduced in previous works.
KW - -semisimple partial -algebras
KW - bounded elements.
KW - topological partial -algebras
KW - -semisimple partial -algebras
KW - bounded elements.
KW - topological partial -algebras
UR - http://hdl.handle.net/10447/62970
M3 - Article
VL - 208
SP - 167
EP - 194
JO - Studia Mathematica
JF - Studia Mathematica
SN - 0039-3223
ER -