GEOMETRIC, SPECTRAL AND ASYMPTOTIC PROPERTIES OF AVERAGED PRODUCTS OF PROJECTIONS IN BANACH SPACES

Catalin Badea (1, 2) , Yuri I Lyubich

1 Université de Lille
2 LPP - Laboratoire Paul Painlevé - UMR 8524

According to the von Neumann-Halperin and Lapidus theorems, in a Hilbert space the iterates of products or, respectively, of convex combinations of orthoprojections are strongly convergent. We extend these results to the iterates of convex combinations of products of some projections in a complex Banach space. The latter is assumed uniformly convex or uniformly smooth for the orthoprojections, or reflexive for more special projections, in particular, for the hermitian ones. In all cases the proof of convergence is based on a known criterion in terms of the boundary spectrum.

Mots clés: orthoprojections; Apostol modulus; boundary spectrum

Domaines: Analyse fonctionnelle [math.FA]

Catalin Badea, Yuri I Lyubich. GEOMETRIC, SPECTRAL AND ASYMPTOTIC PROPERTIES OF AVERAGED PRODUCTS OF PROJECTIONS IN BANACH SPACES. Studia Mathematica, 2010, 201 (1), pp.21-35. ⟨hal-03494694⟩