Operators That Attain their Minima

Abstract

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.

18 pages. arXiv admin note: substantial text overlap with arXiv:1007.1477