Automatic continuity of operators commuting with translations

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

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

Studia Mathematica, Tome 173 (2006), p. 259-293 / Harvested from The Polish Digital Mathematics Library

Résumé

Let $τ_{X}$ and $τ_{Y}$ be representations of a topological group G on Banach spaces X and Y, respectively. We investigate the continuity of the linear operators Φ: X → Y with the property that $Φ \circ τ_{X} (t) = τ_{Y} (t) \circ Φ$ for each t ∈ G in terms of the invariant vectors in Y and the automatic continuity of the invariant linear functionals on X.

Publié le : 2006-01-01

Zbl 1102.46030

EUDML-ID : urn:eudml:doc:284996

@article{bwmeta1.element.bwnjournal-article-doi-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},
     volume = {173},
     year = {2006},
     pages = {259-293},
     zbl = {1102.46030},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm173-3-3}
}

J. Alaminos; J. Extremera; A. R. Villena. Automatic continuity of operators commuting with translations. Studia Mathematica, Tome 173 (2006) pp. 259-293. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm173-3-3/