Abstract
In the present paper, we introduce Euler sequence spaces e r0 and e r c of nonabsolute type that are BK-spaces including the spaces c 0 and c and prove that the spaces e r0 and e r c are linearly isomorphic to the spaces c 0 and c, respectively. Furthermore, some inclusion theorems are presented. Moreover, the α-, β-, γ- and continuous duals of the spaces e r0 and e r c are computed and their bases are constructed. Finally, necessary and sufficient conditions on an infinite matrix belonging to the classes \(\left( {e_c^r :\ell _p } \right)\) and \(\left( {e_c^r :c} \right)\) are established, and characterizations of some other classes of infinite matrices are also derived by means of a given basic lemma, where 1 ≤ p ≤ ∞.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 1, pp. 3–17, January, 2005.
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Altay, B., Basar, F. On Some Euler Sequence Spaces of Nonabsolute Type. Ukr Math J 57, 1–17 (2005). https://doi.org/10.1007/s11253-005-0168-9
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DOI: https://doi.org/10.1007/s11253-005-0168-9