The one-sided ergodic Hilbert transform in Banach spaces
Guy Cohen ; Christophe Cuny ; Michael Lin
Studia Mathematica, Tome 196 (2010), p. 251-263 / Harvested from The Polish Digital Mathematics Library
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Let T be a power-bounded operator on a (real or complex) Banach space. We study the convergence of the one-sided ergodic Hilbert transform limn∑k=1n(Tkx)/k. We prove that weak and strong convergence are equivalent, and in a reflexive space also supn||∑k=1n(Tkx)/k||<∞ is equivalent to the convergence. We also show that -∑k=1∞(Tk)/k (which converges on (I-T)X) is precisely the infinitesimal generator of the semigroup (I-T)|(I-T)X¯r.

Publié le : 2010-01-01
EUDML-ID : urn:eudml:doc:285703 
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Guy Cohen; Christophe Cuny; Michael Lin. The one-sided ergodic Hilbert transform in Banach spaces. Studia Mathematica, Tome 196 (2010) pp. 251-263. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm196-3-3/