Segments of bounded idempotents on a Hilbert space.
Langue
en
Article de revue
Ce document a été publié dans
Journal of Functional Analysis. 2005, vol. 229, n° 2, p. 405-423
Elsevier
Résumé en anglais
Let H be a separable Hilbert space. We prove that any two homotopic idempotents in the algebra may be connected by a piecewise affine idempotent-valued path consisting of 4 segments at most. Moreover, we show that this ...Lire la suite >
Let H be a separable Hilbert space. We prove that any two homotopic idempotents in the algebra may be connected by a piecewise affine idempotent-valued path consisting of 4 segments at most. Moreover, we show that this constant is optimal provided H has infinite dimension. We also explain how this result is linked to the problem of finding common complements for two closed subspaces of H.< Réduire
Mots clés en anglais
idempotent
projection
piecewise affine homotopy
Hilbert space geometry
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