Automatic continuity of operators commuting with translations
Volume 173 / 2006
Studia Mathematica 173 (2006), 259-293
MSC: 46H40, 43A20, 43A40.
DOI: 10.4064/sm173-3-3
Abstract
Let $\tau _X$ and $\tau _Y$ be representations of a topological group $G$ on Banach spaces $X$ and $Y$, respectively. We investigate the continuity of the linear operators ${{\mit\Phi} : X\rightarrow Y}$ with the property that ${\mit\Phi} \circ \tau _X(t)=\tau _Y(t)\circ {\mit\Phi} $ for each $t\in G$ in terms of the invariant vectors in $Y$ and the automatic continuity of the invariant linear functionals on $X$.
