A BANACH PRINCIPLE FOR L-INFINITY

For 1 less than or equal to p < infinity, the classical L(p) Banach Pr inciple relates a.e. convergence of a sequence of operators to the fin iteness of a maximal function, and has had many important applications . For p = infinity, the classical Banach principle has not been as eff ective. We give a formulation of an L(infinity) Banach principle which can be used to establish a.e. convergence (or divergence) of a sequen ce of operators on L(infinity). (C) 1996 Academic Press, Inc.