Abstract: In this paper,we characterize some geometrical properties and some special operators of Banach space by using basic sequence, and get some good results, such as:For a bounded linear operator T:X→Y,T is an isomorphism iff for every basic sequence {x_n}₁ in X, T|_[xt]t=1^∞ is an isomorphism; we also get some characters of compact operator T:c₀→X.

Key words: Compact operator, isomorphism, basic sequence