On the power boundedness of certain Volterra operator pencils

Dashdondog Tsedenbayar. "On the power boundedness of certain Volterra operator pencils." Studia Mathematica 156.1 (2003): 59-66. <http://eudml.org/doc/284894>.

@article{DashdondogTsedenbayar2003,
abstract = {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.},
author = {Dashdondog Tsedenbayar},
journal = {Studia Mathematica},
keywords = {Volterra operator; power-bounded operator; resolvent},
language = {eng},
number = {1},
pages = {59-66},
title = {On the power boundedness of certain Volterra operator pencils},
url = {http://eudml.org/doc/284894},
volume = {156},
year = {2003},
}

TY - JOUR
AU - Dashdondog Tsedenbayar
TI - On the power boundedness of certain Volterra operator pencils
JO - Studia Mathematica
PY - 2003
VL - 156
IS - 1
SP - 59
EP - 66
AB - 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.
LA - eng
KW - Volterra operator; power-bounded operator; resolvent
UR - http://eudml.org/doc/284894
ER -