We give a simple proof of the relation between the spectra of the difference and product of any two idempotents in a Banach algebra. We also give the relation between the spectra of their sum and product.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm148-1-1, author = {Mohamed Barraa and Mohamed Boumazgour}, title = {Spectra of the difference, sum and product of idempotents}, journal = {Studia Mathematica}, volume = {147}, year = {2001}, pages = {1-3}, zbl = {0999.47003}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm148-1-1} }
Mohamed Barraa; Mohamed Boumazgour. Spectra of the difference, sum and product of idempotents. Studia Mathematica, Tome 147 (2001) pp. 1-3. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm148-1-1/