This is an announcement for the paper "One side James' Compactness Theorem" by Bernardo Cascales, Jose Orihuela and Antonio Perez. Abstract: We present some extensions of classical results that involve elements of the dual of Banach spaces, such as Bishop-Phelp's theorem and James' compactness theorem, but restricting to sets of functionals determined by geometrical properties. The main result, which answers a question posed by F. Delbaen, is the following: Let $E$ be a Banach space such that $(B_{E^\ast}, \omega^\ast)$ is convex block compact. Let $A$ and $B$ be bounded, closed and convex sets with distance $d(A,B) > 0$. If every $x^\ast \in E^\ast$ with \[ \sup(x^\ast,B) < \inf(x^\ast,A) \] attains its infimum on $A$ and its supremum on $B$, then $A$ and $B$ are both weakly compact. We obtain new characterizations of weakly compact sets and reflexive spaces, as well as a result concerning a variational problem in dual Banach spaces. Archive classification: math.FA Mathematics Subject Classification: 46A50, 46B50 Remarks: 18 pages Submitted from: antonio.perez7@um.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1508.00496 or http://arXiv.org/abs/1508.00496