A note on the Schur and Phillips lemmas

It is well-known that every weakly convergent sequence in ℓ 1 the norm topology (Schur's lemma). Phillips' lemma asserts even more strongly if a ( μ n ) ∈ N ∞ ′ converges pointwise on { 0 , } to 0, then its -projection 0. In this note we show how second category version of Schur's lemma, for which short proof included, can be used replace by any subsets contains all finite sets and having some kind interpolation property sets.