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

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

2010-06-10

arxiv.org/abs/1006.2052v2

Mathematics

Functional Analysis

the new version incorporates the remarks of the referee ; to appear in Studia Math

Scientific paper

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.

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