# Non-reflexive Banach space s.t. X,X*,X**,... are separable

Is there an infinite-dimensional Banach space $X$, which is not reflexive, such that all the spaces $X,X^{\ast},X^{\ast\ast}, X^{\ast\ast\ast},\dots$ are separable?

• Yes, James space has $X^{**}/X$ of dimension $1$. For example en.wikipedia.org/wiki/James%27_space Also mathoverflow.net/a/43987/454 Feb 8, 2015 at 13:40