An elementary proof of Komlós-Révész theorem in Hilbert spaces.
Guessous, Mohamed (1997)
Journal of Convex Analysis
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Guessous, Mohamed (1997)
Journal of Convex Analysis
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E. Odell, Th. Schlumprecht (1993)
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Lothar Göttsche (1990)
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Petruševski, Ljiljana (1989)
Publications de l'Institut Mathématique. Nouvelle Série
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S. Kwapien (1972-1973)
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We characterize Hilbert spaces among Banach spaces in terms of transitivity with respect to nicely behaved subgroups of the isometry group. For example, the following result is typical: If X is a real Banach space isomorphic to a Hilbert space and convex-transitive with respect to the isometric finite-dimensional perturbations of the identity, then X is already isometric to a Hilbert space.
Eberhard Gerlach (1971)
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A general theorem on Hilbert subspaces of dually nuclear spaces is proved, from which all previous results of K. Maurin and the writer on regularity of generalized eigenfunctions follow as simple corollaries. In addition some supplements to L. Schwartz’s work on Hilbert subspaces in spaces of smooth functions are given.
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Let X and Y be two closed subspaces of a Hilbert space. If we send a point back and forth between them by orthogonal projections, the iterates converge to the projection of the point onto the intersection of X and Y by a theorem of von Neumann. Any sequence of orthoprojections of a point in a Hilbert space onto a finite family of closed subspaces converges weakly, according to Amemiya and Ando. The problem of norm convergence was open for a long time. Recently Adam...