KONIG CHAINS FOR SUBMULTIPLICATIVE FUNCTIONS AND INFINITE PRODUCTS OF OPERATORS

摘要

We generalize the so-called Weighted Konig Lemma, due to Mate, for a submultiplicative function oil a subset of the union U-n is an element of N Sigma(n), where Sigma is a set and Sigma(n) is the Cartesian product of n copies of Sigma Instead of a combinatorial argument its done by Mate, our proof uses Tychonoff's compactness theorem to show the existence of a Konig chain for it submultiplicative function. As a consequence, we obtain an extension of the Daubechies-Lagarias theorem concerning it finite set Sigma of matrices with right convergent products. Here we replace matrices by Banach algebra elements, and we substitute compactness for finiteness of Sigma The last result yields new generalizations of the Kehsky-Rivlm theorem on iterates of the Bernstein operators on the Banach space C[0.1]