For Banach Jordan algebras and pairs the spectrum is proved to be related to the spectrum in a Banach algebra. Consequently, it is an analytic multifunction, upper semicontinuous with a dense G delta-set of points of continuity, and the scarcity theorem holds.
@article{urn:eudml:doc:40317, title = {Analytic properties of the spectrum in Banach Jordan Systems.}, journal = {Collectanea Mathematica}, volume = {47}, year = {1996}, pages = {277-284}, zbl = {0865.46034}, mrnumber = {MR1437656}, language = {en}, url = {http://dml.mathdoc.fr/item/urn:eudml:doc:40317} }
Hessenberger, Gerald. Analytic properties of the spectrum in Banach Jordan Systems.. Collectanea Mathematica, Tome 47 (1996) pp. 277-284. http://gdmltest.u-ga.fr/item/urn:eudml:doc:40317/