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Displaying similar documents to “Special symmetries of Banach spaces isomorphic to Hilbert spaces”

Snakes and articulated arms in an Hilbert space

Fernand Pelletier, Rebhia Saffidine (2013)

Annales de la faculté des sciences de Toulouse Mathématiques

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The purpose of this paper is to give an illustration of results on integrability of distributions and orbits of vector fields on Banach manifolds obtained in [5] and [4]. Using arguments and results of these papers, in the context of a separable Hilbert space, we give a generalization of a Theorem of accessibility contained in [3] and [6] for articulated arms and snakes in a finite dimensional 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.

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.