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Ferreira, M. A. M. (2020). Some considerations on orthogonality, strict separation theorems and applications in Hilbert spaces. In Le Bin Ho (Ed.), Hilbert spaces: Properties and applications. (pp. 1-19). New York: Nova Science Publishers, Inc.
M. A. Ferreira, "Some considerations on orthogonality, strict separation theorems and applications in Hilbert spaces", in Hilbert spaces: Properties and applications, Le Bin Ho, Ed., New York, Nova Science Publishers, Inc., 2020, pp. 1-19
@incollection{ferreira2020_1724525540029, author = "Ferreira, M. A. M.", title = "Some considerations on orthogonality, strict separation theorems and applications in Hilbert spaces", chapter = "", booktitle = "Hilbert spaces: Properties and applications", year = "2020", volume = "", series = "Mathematics research developments", edition = "", pages = "1-1", publisher = "Nova Science Publishers, Inc.", address = "New York", url = "https://novapublishers.com/shop/hilbert-spaces-properties-and-applications/" }
TY - CHAP TI - Some considerations on orthogonality, strict separation theorems and applications in Hilbert spaces T2 - Hilbert spaces: Properties and applications AU - Ferreira, M. A. M. PY - 2020 SP - 1-19 CY - New York UR - https://novapublishers.com/shop/hilbert-spaces-properties-and-applications/ AB - After presenting some structural notions on Hilbert spaces, which constitute fundamental support for this work, we approach the goals of thechapter. First,studyaboutconvexsets,projections,andorthogonality, whereweapproachtheoptimizationprobleminHilbertspaceswithsome generality. Then the approach to Riesz 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. These theorems are very important in the applications. Moreover, the presented strict separation theorems and the Riesz representation theorem have key importance in the demonstrations of Kuhn-Tucker and minimax theorems and respective corollaries. ER -