Hyperexpansive weighted translation semigroups
Volume 159 / 2020
Colloquium Mathematicum 159 (2020), 157-169
MSC: Primary 47B20, 47B37; Secondary 47A10, 46E22.
DOI: 10.4064/cm7583-12-2018
Published online: 26 September 2019
Abstract
Weighted shift operators turn out to be extremely useful in supplying interesting examples of operators on Hilbert spaces. With a view to studying continuous analogues of weighted shifts, M. Embry and A. Lambert initiated the study of operator semigroups $\{S_t\}$ indexed by non-negative real numbers and termed weighted translation semigroups, where the operators $S_t$ are defined on $L^2(\mathbb R_+)$ by using a weight function. We obtain characterizations of hyperexpansive weighted translation semigroups in terms of their symbols. We also discuss the Cauchy dual of a hyperexpansive weighted translation semigroup. As an application, we present new proofs of a couple of known results.
