Geodesic
Characterizing weak-operator continuous linear functionals on $B(H)$ constructively
Documenta mathematica, Tome 16 (2011), pp. 597-617
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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⇝〈Tx,y〉. We also prove that the identification of weak- and strong-operator continuous linear functionals on B(H) cannot be established constructively.
DOI : 10.4171/dm/344
Classification : 03F60, 46S30, 47L50
Mots-clés : constructive, operators, (ultra)weak operator topology, continuous functionals 
@article{10_4171_dm_344,
     author = {Douglas S. Bridges},
     title = {Characterizing weak-operator continuous linear functionals on $B(H)$ constructively},
     journal = {Documenta mathematica},
     pages = {597--617},
     year = {2011},
     volume = {16},
     doi = {10.4171/dm/344},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/344/}
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Douglas S. Bridges. Characterizing weak-operator continuous linear functionals on $B(H)$ constructively. Documenta mathematica, Tome 16 (2011), pp. 597-617. doi: 10.4171/dm/344

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