Abstract
In the present paper, we introduce Euler sequence spaces e 0 r and e of nonabsolute type that are BK-spaces including the spaces c 0 and c and prove that the spaces e 0 r and e 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 0 r and e 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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