On the degree of polynomials connecting two idempotents of a Banach algebra. (English) Zbl 0853.46044
Summary: We show the existence of a constant \(M\) such that, given any \(C^*\)-algebra, any two elements \(a\), \(b\) in the same component of the set of idempotents of that \(C^*\)-algebra, we can find a (idempotent-valued) polynomial of degree lower than \(M\) connecting \(a\) and \(b\).