Characterizing filters by convergence (with respect to filters) in Banach spaces

Let X be a topological space and let F be a filter on N, recall that a sequence (x(n))(n is an element of N) in X is said to be F-convergent to the point x is an element of X, if for each neighborhood U of x, (n is an element of N: x(n) is an element of U} is an element of F. By using F-convergence in l(1) and in Banach spaces, we characterize the P-filters, the P-filters(+), the weak P-filters, the Q-filters, the Q-filters(+), the weak Q-filters, the selective filters and the selective(+) filters. (C) 2012 Elsevier B.V. All rights reserved.