Sequence space of convergent series can also be seen as a matrix domain of triangle. By using the theory of matrix domains of triangle, as well as the fact that cs is an AK space we can give the representation of some general bounded linear operators related to the cs sequence space. We will also give the conditions for compactness by using the Hausdorff measure of noncompactness. 1. Basic Notations The set ω will denote all complex sequences x = (x k) ∞ k=0 and ∞ , c, c 0 and φ will denote the sets of all bounded, convergent, null and finite sequences. As usual, let e and e (n) ,(n = 0, 1, ...) represent the sequences with e k = 1 for all k, and e (n) n = 1 and e (n) k = 0 for k n. A sequence (b n) ∞ n=0 in a linear metric space X is called a Schauder basis if for every x ∈ X exists a unique sequence (λ n) ∞ n=0 of scalars such that x = ∞ n=0 λ n b n. A subspace X of ω is called an FK space if it is a complete linear metric space with continuous coordinates P n : X → C , (n = 0, 1, ...) where P n (x) = x n. An FK space X ⊃ φ is said to have AK if his Schauder basis is (e (n)) ∞ n=0 , and a normed FK space is BK space. The spaces c 0 , c, l ∞ are all the BK spaces and among them only the c 0 has AK. The space ∞ has no Schauder base. Let A = (a nk) ∞ n,k=0 be an infinite matrix of complex numbers, and X and Y be subsets of ω. We denote with A n = (a nk) ∞ k=0 the sequences in the n-th row of A, A n x = ∞ k=0 a nk x k and Ax = (A n x) ∞ n=0 (provided all the series A n x converge). Matrix domain of A in X is X A = {x ∈ ω|Ax ∈ X} and (X, Y) is the class of all matrices A such that X ⊂ Y A. If (X, ·) is a normed space we write S X for unit sphere and B X for the closed unit ball in X. For X ⊃ φ a BK space and a = (a k) ∈ ω we define a * X = sup x∈S X | ∞ k=0 a k x k | provided the right side exists and is finite. β-dual of X, X β , is the set defined with X β = {a = (a k) ∈ ω| ∞ k=0 a k x k converes , ∀x ∈ X}. It is clear that β-duals play important role since A ∈ (X, Y) if and only if A n ∈ X β for all n and Ax ∈ Y for all x ∈ X. We write B(X, Y) for the set of all bounded linear operators. An infinite matrix T = (t nk) ∞ n,k=0 is said to be a triangle if t nk = 0 for k > n and t nn 0, (n = 0, 1, ...). It is well-known that every triangle T has a unique inverse S = (S nk) ∞ n,k=0 which also is a triangle, and x = T(S(x)) = S(T(x)) for all x ∈ ω.