Geometric, spectral and asymptotic properties of averaged products of projections in Banach spaces

• Autorzy: Catalin Badea , Yuri I. Lyubich
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47A05: General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
• 46B20: Geometry and structure of normed linear spaces
• 47A10: Spectrum, resolvent

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2010
• Tom: 201
• Numer: 1
• Strony: 21-35

Daty

wydano

2010

Twórcy

autor

Catalin Badea

• Laboratoire Paul Painlevé, Université Lille 1, CNRS UMR 8524, Bât. M2, F-59655 Villeneuve d'Ascq Cedex, France

autor

Yuri I. Lyubich

• Department of Mathematics, Technion, 32000, Haifa, Israel

Identyfikatory

DOI

10.4064/sm201-1-2