A lemma on matrices and its applications

On Antosik’s Lemma and the Antosik-Mikusinski Basic Matrix Theorem

“…In [1] and [2], Antosik proved two results which are called the Antosik-Mikusinski Basic Matrix Theorem and Antosik's Lemma, respectively. The theorem and lemma have been proven to be quite effective in treating various topics in Functional Analysis and Set Function Theory [1]- [6].…”

“…Antosik observed that assumption (i) can be dropped if G is a locally convex space and posed the problem ( [2]) of whether (i) can also be dropped in general. In [8], Weber solved this problem showing that assumption (i) is in fact superfluous.…”

Invariants in abstract mapping pairs

“…[1],[11, page 12]). Let G be an abelian topological group and let x t j e Gfori,j e N. Ifeach subsequence {m,-} of'{/} has a further subsequence {«,} such that(1) linv+oo*^,,, = Oforj e N and (2) lim^oo YlJLi x n,n, = 0, then Xn -> 0.…”