A smooth, non-reflexive second conjugate space

A Non-Reflexive Banach Space Isometric With Its Second Conjugate Space.

A Banach space B is isometric with a subspace of its second conjugate space B** under the "natural mapping" for which the element of B** which corresponds to the element xo of B is the linear functional Fxz defined by Fxs(f) = f(xo) for each f of B*. If every F of B** is of this form, then B is said to be reflexive and B is isometric with B** under this natural mapping. The purpose of this note...

A non-reflexive Banach space with all contractions mean ergodic

We construct on any quasi-reflexive of order 1 separable real Banach space an equivalent norm, such that all contractions on the space and all contractions on its dual are mean ergodic, thus answering negatively a question of Louis Sucheston.

A Non-reflexive Whitehead Group

We prove that it is consistent that there is a non-reflexive Whitehead group, in fact one whose dual group is free. We also prove that it is consistent that there is a group A such that Ext(A,Z) is torsion and Hom(A,Z) = 0. As an application we show the consistency of the existence of new co-Moore spaces.

Every Banach Space is Reflexive

The title above is wrong, because the strong dual of a Banach space is too strong to assert that the natural correspondence between a space and its bidual is an isomorphism. This, from a categorical point of view, is indeed the right duality concept because it yields a self adjoint dualisation functor. However, for many applications the non–reflexiveness problem can be solved by replacing the n...

Chinese Reflexive Ziji in Second Language Acquisition