Segments of bounded idempotents on a Hilbert space.

Julien Giol (1)

1 LaBAG - Laboratoire Bordelais d'Analyse et Géométrie

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.

Mots clés: idempotent; projection; piecewise affine homotopy; Hilbert space geometry

Domaines: Analyse fonctionnelle [math.FA]

Julien Giol. Segments of bounded idempotents on a Hilbert space.. Journal of Functional Analysis, 2005, 229 (2), pp.405-423. ⟨hal-00288807⟩