Some Considerations on Orthogonality, Strict Separation Theorems and Applications in Hilbert Spaces - Ferreira, M. A. M. (EasyChair Preprint Nº 7894, 2025)
After presenting some structural notions on Hilbert spaces, which constitute a fundamental support for this work, we approach the goals of the chapter. First, a study about convex sets, projections and orthogonality, where we approach the optimization problem in Hilbert spaces with some generality. Then the approach to Riez representation theorem in this field, important in the rephrasing of the separation theorems. Then we give a look to the strict separation theorems as well as to the main results of convex programming: Kuhn-Tucker theorem and minimax theorem. Both these theorems are very important in the applications. Moreover, the strict separation theorems presented and the Riez representation theorem have a key importance in the demonstrations of Kuhn-Tucker and minimax theorems and respective corollaries.