Using axiomatic joint spectra we obtain a functional calculus which extends our previous Gelfand-Waelbroeck type results to include a Banach-valued Taylor-Waelbroeck spectrum.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm175-3-2, author = {S. Se\'an and Robin E. Harte}, title = {Banach-valued axiomatic spectra}, journal = {Studia Mathematica}, volume = {173}, year = {2006}, pages = {213-232}, zbl = {1115.46037}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm175-3-2} }
S. Seán; Robin E. Harte. Banach-valued axiomatic spectra. Studia Mathematica, Tome 173 (2006) pp. 213-232. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm175-3-2/