On Some Euler Sequence Spaces of Nonabsolute Type - Altay, B.; Başar, F. (Ukrains’kyi Matematychnyi Zhurnal, 2005)
In the present paper, the Euler sequence spaces e_0^r and e^r_c of nonabsolute type which are the BK-spaces including the spaces c_0 and c have been introduced and proved that the spaces e_0^r and e^r_c are linearly i somorphic to the spaces c_0 and c, respectively. Furthemore, some inclusion theorems have been given. Additionally, the α-, β-, γ- and continuous duals of the spaces e_0^r and e^r_c have been computed and their basis have been constructed. Finally, the necessary and sufficient conditions on an infinite matrix belonging to the classes (e^r_c : l_p) and (e^r_c : c) have been determined and the characterizations of some other classes of infinite matrices have also been derived by means of a given basic lemma, where 1 ≤ p ≤ ∞.