Automatic continuity of operators commuting with translations

J. Alaminos ¹   ; J. Extremera ¹   ; A. R. Villena ¹

¹ Departamento de Análisis Matemático Facultad de Ciencias Universidad de Granada 18071 Granada, Spain

Studia Mathematica, Tome 173 (2006) no. 3, pp. 259-293

Résumé

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 $X$.

Détail

DOI : 10.4064/sm173-3-3

Keywords: tau tau representations topological group banach spaces respectively investigate continuity linear operators mit phi rightarrow property mit phi circ tau tau circ mit phi each terms invariant vectors automatic continuity invariant linear functionals