Non-supercyclicity of Volterra convolution and related operators

TY - JOUR

T1 - Non-supercyclicity of Volterra convolution and related operators

AU - Eveson, Simon

PY - 2008/12

Y1 - 2008/12

N2 - We show that if V-alpha (alpha > 0) is the Riemann-Liouville fractional integration operator and T is an invertible operator on L-2(0, 1) which commutes with V, then TV alpha is not supercyclic on L-2(0, 1); in particular, many Volterra convolution operators are not supercyclic. The technique is based on an argument used by Gallardo-Gutierrez and Montes-Rodriguez to show that V is not supercyclic.

AB - We show that if V-alpha (alpha > 0) is the Riemann-Liouville fractional integration operator and T is an invertible operator on L-2(0, 1) which commutes with V, then TV alpha is not supercyclic on L-2(0, 1); in particular, many Volterra convolution operators are not supercyclic. The technique is based on an argument used by Gallardo-Gutierrez and Montes-Rodriguez to show that V is not supercyclic.

KW - Supercyclic

KW - Volterra convolution

KW - fractional integration operator

UR - http://www.scopus.com/inward/record.url?scp=58149133923&partnerID=8YFLogxK

U2 - 10.1007/s00020-008-1625-2

DO - 10.1007/s00020-008-1625-2

M3 - Article

SN - 0378-620X

VL - 62

SP - 585

EP - 589

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

IS - 4

ER -