We show that a real Banach algebra A such that ||a²|| = ||a||² for a ∈ A is a subalgebra of the algebra of continuous quaternion-valued functions on a compact set X.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm162-3-2, author = {Mati Abel and Krzysztof Jarosz}, title = {Noncommutative uniform algebras}, journal = {Studia Mathematica}, volume = {162}, year = {2004}, pages = {213-218}, zbl = {1054.46031}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm162-3-2} }
Mati Abel; Krzysztof Jarosz. Noncommutative uniform algebras. Studia Mathematica, Tome 162 (2004) pp. 213-218. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm162-3-2/