In this paper, we introduce the spaces ℓ˘∞ℓ˘∞, c˘c˘ and c˘0c˘0 of Euler-Ces`aro bounded, convergent and null difference sequences and prove that the inclusions ℓ∞⊂ℓ˘∞ℓ∞⊂ℓ˘∞, c⊂c˘c⊂c˘ and c0⊂c˘0c0⊂c˘0 strictly hold. We show that the spaces c˘0c˘0 and c˘c˘ turn out to be the separable BK spaces such that c˘c˘ does not possess any of the following: AK property and monotonicity. We determine the alpha-, beta- and gamma-duals of the new spaces and characterize the matrix classes (c˘:ℓ∞)(c˘:ℓ∞), (c˘:c)(c˘:c) and (c˘:c0)(c˘:c0).
