Geodesic
Characterizing weak-operator continuous linear functionals on $B(H)$ constructively
Documenta mathematica, Tome 16 (2011), pp. 597-617.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let $B(H)$ be the space of bounded operators on a not-necessarily-separable Hilbert space $H$. Working within Bishop-style constructive analysis, we prove that certain weak-operator continuous linear functionals on $B(H)$ are finite sums of functionals of the form $T\rightsquigarrowleftlangle Tx,y\right\rangle $. We also prove that the identification of weak- and strong-operator continuous linear functionals on $B(H)$ cannot be established constructively.
Classification : 03F60, 47L50, 46S30
Keywords: constructive, operators, (ultra)weak operator topology, continuous functionals 
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     author = {Bridges, Douglas S.},
     title = {Characterizing weak-operator continuous linear functionals on $B(H)$ constructively},
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     url = {http://geodesic.mathdoc.fr/item/DOCMA_2011__16__a14/}
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Bridges, Douglas S. Characterizing weak-operator continuous linear functionals on $B(H)$ constructively. Documenta mathematica, Tome 16 (2011), pp. 597-617. http://geodesic.mathdoc.fr/item/DOCMA_2011__16__a14/