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The purpose of this paper is to give a number of characterizations of reflexive Banach spaces having Schauder bases. We show that a Banach space $ X$ is contained in either $ X$ $ {X^{\ast}}$. It follows that a Banach space with an unconditional basis is reflexive if and only if no basis is of type . It is also shown that a Banach space with a basis is reflexive if and only if every basis converges weakly to zero.

Let X and Y denote Banach spaces with bases $ ({x_i})$, respectively, and let $ X{ \otimes _\varepsilon }Y$ $ X{ \otimes _\pi }Y$ $ \varepsilon $ crossnorms of the algebraic tensor product $ X \otimes Y$ The purpose of this paper is to study the structure of the tensor product spaces $ X{ \otimes _\varepsilon }Y$ $ X{ \otimes _\pi }Y$ $ ({x_i} \otimes {y_j})$ of such bases.