caa a22 4500 467979391 CHVBK 20180323112515.0 cr unu---uuuuu 170328e19900201xx s 000 0 eng 10.1007/BF02862879 doi (NATIONALLICENCE)springer-10.1007/BF02862879 Pannenberg Michael Mathematisches Institut der Westfälischen Wilhelms-Universität, Einsteinstrasse 62, D-4400, Muenster, Federal Republic of Germany aut Some remarks on spectral states of LMC -algebras [Elektronische Daten] [Michael Pannenberg] We generalize the notion of a spectral state (as introduced for Banach algebras by Moore, Bonsall and Duncan) to the context of locally multiplicatively-convex (LMC) algebras by proceeding in a way analogous to the generalization of numerical range theory from Banach algebras toLMC-algebras carried out by Giles and Koehler. Among the results obtained in this note are integral representations of spectral states by probability measures on the structure space ofA and the determination of the extreme points of the convex set $$\Omega _A $$ of all spectral states on a commutativeLMC-algebraA (which is related to different Choquet boundaries) as well as a characterization of symmetric involutions by the coincidence of the notions of positive state and spectral state and a characterization of theQ-property by the weak-*-boundedness of $$\Omega _A $$ . The paper finishes with two elementary commutativity criteria involving spectral states and two Korovkin-type theorems for the approximation of unital algebra homomorphisms by σ-equicontractive nets of linear operators mapping anLMC-algebraA into theLMC-algebra of all continuous complex-valued functions on a completely regular spaceX. Springer, 1990 Rendiconti del Circolo Matematico di Palermo Springer-Verlag 39/1(1990-02-01), 79-98 0009-725X 39:1<79 1990 39 12215 https://doi.org/10.1007/BF02862879 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02862879 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Pannenberg Michael Mathematisches Institut der Westfälischen Wilhelms-Universität, Einsteinstrasse 62, D-4400, Muenster, Federal Republic of Germany aut NATIONALLICENCE 773 0- Rendiconti del Circolo Matematico di Palermo Springer-Verlag 39/1(1990-02-01), 79-98 0009-725X 39:1<79 1990 39 12215 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer