Time regularity and functions of the Volterra operator
Volume 220 / 2014
Studia Mathematica 220 (2014), 1-14
MSC: Primary 47A10, 47A30, 47B38; Secondary 47G10.
DOI: 10.4064/sm220-1-1
Abstract
Our aim is to prove that for any fixed $1/2 < \alpha < 1$ there exists a Hilbert space contraction $T$ such that $\sigma(T) = \{1\}$ and $$ \|T^{n+1} - T^n\| \asymp n^{-\alpha} \quad (n \geq 1). $$ This answers Zemánek's question on the time regularity property.
