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Miklos Schweitzer 1967_6

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October 6, 2008
vectorFunctional Analysisreal analysisreal analysis unsolved

Problem Statement

Let A A be a family of proper closed subspaces of the Hilbert space H\equal{}l^2 totally ordered with respect to inclusion (that is , if L1,L2∈A L_1,L_2 \in A, then either L1⊂L2 L_1\subset L_2 or L2⊂L1 L_2\subset L_1). Prove that there exists a vector x∈H x \in H not contaied in any of the subspaces L L belonging to A A. B. Szokefalvi Nagy
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