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

Catalin Badea, and Yuri I. Lyubich. "Geometric, spectral and asymptotic properties of averaged products of projections in Banach spaces." Studia Mathematica 201.1 (2010): 21-35. <http://eudml.org/doc/285914>.

@article{CatalinBadea2010,
abstract = {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.},
author = {Catalin Badea, Yuri I. Lyubich},
journal = {Studia Mathematica},
language = {eng},
number = {1},
pages = {21-35},
title = {Geometric, spectral and asymptotic properties of averaged products of projections in Banach spaces},
url = {http://eudml.org/doc/285914},
volume = {201},
year = {2010},
}

TY - JOUR
AU - Catalin Badea
AU - Yuri I. Lyubich
TI - Geometric, spectral and asymptotic properties of averaged products of projections in Banach spaces
JO - Studia Mathematica
PY - 2010
VL - 201
IS - 1
SP - 21
EP - 35
AB - 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.
LA - eng
UR - http://eudml.org/doc/285914
ER -