RESUMEN

This is a study of the space of idempotent elements of banach algebra, and its “grassmannian”. The last term needs explanation: if p and q are idempotent operators, then they have the same range if and only if pq = q and qp = p. These equalities define always an equivalence relation among the idempotents of an arbitrary algebra, whose classes become therefore substitutes for the range. The space of classes is called the grassmannian of the given algebra. The reason is that the grassmannian of the algebra of all linear endomorphisms of a finite dimensional vector space is nothing but the union of all the ordinary grassmann varieties of a given total dimension, the components being the usual G_{n-m, m}  0<= m <= n.