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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Eberhard Gerlach (1971)
Annales de l'institut Fourier
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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.
Kryukov, Alexey A. (2005)
International Journal of Mathematics and Mathematical Sciences
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Stanley Gudder (1986)
Annales de l'I.H.P. Physique théorique
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S. Pilipović (1987)
Rendiconti del Seminario Matematico della Università di Padova
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Migórski, S. (1995)
Journal of Applied Mathematics and Stochastic Analysis
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Lothar Göttsche (1990)
Manuscripta mathematica
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Eva Kopecká, Vladimír Müller (2014)
Studia Mathematica
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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...
J. Płonka (1977)
Colloquium Mathematicae
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S. Kwapien (1972-1973)
Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")
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N. J. Kalton (2008)
Studia Mathematica
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We show that if X is an infinite-dimensional Banach space in which every finite-dimensional subspace is λ-complemented with λ ≤ 2 then X is (1 + C√(λ-1))-isomorphic to a Hilbert space, where C is an absolute constant; this estimate (up to the constant C) is best possible. This answers a question of Kadets and Mityagin from 1973. We also investigate the finite-dimensional versions of the theorem.
E. Odell, Th. Schlumprecht (1993)
Geometric and functional analysis
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