On the closure of the sum of closed subspaces

Autor: Irwin E. Schochetman, Robert L. Smith, Sze-Kai Tsui
Jazyk: angličtina
Rok vydání: 2001
Předmět:
Zdroj: International Journal of Mathematics and Mathematical Sciences, Vol 26, Iss 5, Pp 257-267 (2001)
Druh dokumentu: article
ISSN: 0161-1712
1687-0425
01611712
DOI: 10.1155/S0161171201005324
Popis: We give necessary and sufficient conditions for the sum of closed subspaces of a Hilbert space to be closed. Specifically, we show that the sum will be closed if and only if the angle between the subspaces is not zero, or if and only if the projection of either space into the orthogonal complement of the other is closed. We also give sufficient conditions for the sum to be closed in terms of the relevant orthogonal projections. As a consequence, we obtain sufficient conditions for the existence of an optimal solution to an abstract quadratic programming problem in terms of the kernels of the cost and constraint operators.
Databáze: Directory of Open Access Journals
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