%0 Journal Article %T Operators That Attain their Minima %A Xavier Carvajal %A Wladimir Neves %J Mathematics %D 2013 %I arXiv %X In this paper we study the theory of operators on complex Hilbert spaces, which attain their minimum in the unit sphere. We prove some important results concerning the characterization of the N*, and also AN* operators, see respectively Definition 1.1 and Definition 1.3. The injective property plays an important role in these operators, and shall be established by these classes. %U http://arxiv.org/abs/1304.2684v2