Matrix Transforms into a Set of α-absolutely Aλ-summable Sequences

Suppose A is a matrix having real or complex entries and λ- a monotonically increasing strictly positive sequence, i.e., the speed. In this paper, the notions of λ-reversibility of A, $$Α^λ$$-boundedness, and $$Α^λ$$-summability of sequences are recalled, and the notion of α-absolute $$Α^λ$$-summability of sequences is introduced. Also, there are characterized matrix transforms from the set of all $$Α^λ$$ -bounded, or the set of all α-summable, or the set of all 1- absolute $$Α^λ$$-summable sequences into the set of all α-absolutely (α>1) $$Β^μ$$-summable sequences for a normal or λ-reversible matrix A and a matrix $$Β=(b_{nk})$$ with $$b_{nk}=0$$, k>n, and for another speed μ.