GEOMETRIC, SPECTRAL AND ASYMPTOTIC PROPERTIES ...
Document type :
Compte-rendu et recension critique d'ouvrage
Title :
GEOMETRIC, SPECTRAL AND ASYMPTOTIC PROPERTIES OF AVERAGED PRODUCTS OF PROJECTIONS IN BANACH SPACES
Author(s) :
Badea, Catalin [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Université de Lille
Lyubich, Yuri [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Université de Lille
Lyubich, Yuri [Auteur]
Journal title :
Studia Mathematica
Pages :
21-35
Publisher :
Instytut Matematyczny - Polska Akademii Nauk
Publication date :
2010-06-10
ISSN :
0039-3223
English keyword(s) :
orthoprojections
Apostol modulus
boundary spectrum
Apostol modulus
boundary spectrum
HAL domain(s) :
Mathématiques [math]/Analyse fonctionnelle [math.FA]
English abstract : [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 ...
Show more >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.Show less >
Show more >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.Show less >
Language :
Anglais
Popular science :
Non
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