1Laboratoire Paul Painlevé Université Lille 1 CNRS UMR 8524, Bât. M2 F-59655 Villeneuve d'Ascq Cedex, France 2Department of Mathematics Technion 32000, Haifa, Israel
Studia Mathematica, Tome 201 (2010) no. 1, pp. 21-35
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.
Keywords:
according von neumann halperin lapidus theorems hilbert space iterates products respectively convex combinations orthoprojections strongly convergent extend these results iterates convex combinations products projections complex banach space latter assumed uniformly convex uniformly smooth orthoprojections reflexive special projections particular hermitian cases proof convergence based known criterion terms boundary spectrum
Affiliations des auteurs :
Catalin Badea
1
;
Yuri I. Lyubich
2
1
Laboratoire Paul Painlevé Université Lille 1 CNRS UMR 8524, Bât. M2 F-59655 Villeneuve d'Ascq Cedex, France
2
Department of Mathematics Technion 32000, Haifa, Israel
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Catalin Badea; Yuri I. Lyubich. Geometric, spectral and asymptotic properties of
averaged products of projections in Banach spaces. Studia Mathematica, Tome 201 (2010) no. 1, pp. 21-35. doi: 10.4064/sm201-1-2
