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 $X$.
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
Affiliations des auteurs :
J. Alaminos
1
;
J. Extremera
1
;
A. R. Villena
1
1
Departamento de Análisis Matemático Facultad de Ciencias Universidad de Granada 18071 Granada, Spain
@article{10_4064_sm173_3_3,
author = {J. Alaminos and J. Extremera and A. R. Villena},
title = {Automatic continuity of operators
commuting with translations},
journal = {Studia Mathematica},
pages = {259--293},
year = {2006},
volume = {173},
number = {3},
doi = {10.4064/sm173-3-3},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm173-3-3/}
}
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AU - J. Alaminos
AU - J. Extremera
AU - A. R. Villena
TI - Automatic continuity of operators
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SP - 259
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VL - 173
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commuting with translations
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J. Alaminos; J. Extremera; A. R. Villena. Automatic continuity of operators
commuting with translations. Studia Mathematica, Tome 173 (2006) no. 3, pp. 259-293. doi: 10.4064/sm173-3-3
