is reflexive; the closed unit ball is compact when has the weak topology . is a Banach space and is reflexive. Examples Every non-reflexive infinite-dimensional Banach space is a distinguished space that is not semi-reflexive. If is a dense proper vector subspace of a reflexive Banach space then is a normed space that not semi-reflexive but its strong dual space is a reflexive Banach space. There exists a semi-reflexive countably barrelled space that is not barrelled. See also Grothendieck space - A generalization which has some of the properties of reflexive spaces and includes many spaces of practical importance. Reflexive operator algebra Reflexive space Citations Bibliography John B. Conway, A Course in Functional Analysis, Springer, 1985. . . Banach spaces Duality theories