Displaying similar documents to “On discrete subspaces of a Hilbert space”

Some embedding properties of Hilbert subspaces in topological vector spaces

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.

A product of three projections

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...

The complemented subspace problem revisited

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.

Special symmetries of Banach spaces isomorphic to Hilbert spaces

Jarno Talponen (2010)

Studia Mathematica

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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.