On the power boundedness of certain Volterra operator pencils

• Autorzy: Dashdondog Tsedenbayar
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47A10: Spectrum, resolvent

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2003
• Tom: 156
• Numer: 1
• Strony: 59-66

Daty

wydano

2003

Twórcy

autor

Dashdondog Tsedenbayar

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, P.O. Box 21, 00-956 Warszawa, Poland
• Department of Mathematics, Mongolian Teacher's University, Ulan-Bator, Mongolia

Identyfikatory

DOI

10.4064/sm156-1-4