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

摘要

Let X be a topological space and let F be a filter on N, recall that a sequence (x_n)n∈N in X is said to be F-convergent to the point x∈X, if for each neighborhood U of x, {n ∈N: x_n ∈U) ∈ 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 Qfilters, the selective filters and the selective~+ filters.