Contractive polynomials of the Volterra operator
Volume 240 / 2018
Studia Mathematica 240 (2018), 201-211
MSC: Primary 47B38; Secondary 47B44, 47G10.
DOI: 10.4064/sm8051-5-2017
Published online: 12 October 2017
Abstract
If $\varphi $ is a holomorphic function with $\varphi (0) = 1$ then we present sufficient conditions and necessary conditions for $\varphi (V)$ to be a contraction, where $V$ is the Volterra operator on $L_2(0,1)$. In particular we show that this may happen for certain polynomials $\varphi $, disproving a conjecture by Lyubich and Tsedenbayar.
