On dual of Banach sequence spaces (original) (raw)

J. Hagler and P. Azimi have introduced a class of Banach sequence spaces, the X α,1 spaces as a class of hereditarily 1 Banach spaces. In this paper, we show that (i) X * α,1 , the dual of Banach space X α,1 contains asymptotically isometric copies of ∞, (ii) X * α,1 is nonseparable although X α,1 is a separable Banach space. Also, we show X α,1 is not hereditarily indecomposable. p. Here, using two methods we show that the Banach spaces X * α,1 , the dual of Banach spaces X α,1 , are nonseparable. By the first method, we show X * α,1 contain asymptotically isometric copy of ∞. A result of [6] shows that X * α,1 contain isometric copy of ∞ , and then they are nonseparable. By the second method,