On the power boundedness of certain Volterra operator pencils
Dashdondog Tsedenbayar
Studia Mathematica, Tome 157 (2003), p. 59-66 / Harvested from The Polish Digital Mathematics Library
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Let V be the classical Volterra operator on L²(0,1), and let z be a complex number. We prove that I-zV is power bounded if and only if Re z ≥ 0 and Im z = 0, while I-zV² is power bounded if and only if z = 0. The first result yields ||(I-V)ⁿ-(I-V)n+1||=O(n-1/2) as n → ∞, an improvement of [Py]. We also study some other related operator pencils.

Publié le : 2003-01-01
EUDML-ID : urn:eudml:doc:284894 
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Dashdondog Tsedenbayar. On the power boundedness of certain Volterra operator pencils. Studia Mathematica, Tome 157 (2003) pp. 59-66. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm156-1-4/