F-bases with brackets and with individual brackets in Banach spaces

摘要

We provide a partial answer to the question of Vladimir Kadets whether given an F-basis of a Banach space X, with respect to some filter F ? Ρ (?), the coordinate functionals are continuous. The answer is positive if the character of F is less than p. In this case every F-basis is an M-basis with brackets which are determined by an element of F.