On the Euler sequence spaces which include the spaces ℓpℓp and ℓ∞ℓ∞ II

By epr, we mean the space of all sequences whose Euler transforms of order rr are in the sequence spaces ℓpℓp and ℓ∞ℓ∞ (see [B. Altay, F. Başar, M. Mursaleen, On the Euler sequence spaces which include the spaces ℓpℓp and ℓ∞ℓ∞ I, Inform. Sci. (2005) (in press)]), where 1≤p<∞1≤p<∞. In the present paper, we essentially characterize the classes (epr:ℓ∞),(e1r:ℓp) and (epr:f) of infinite matrices for 1