Characterising Weak-Operator Continuous Linear Functionals on $B(H)$ constructively

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.

2010 Mathematics Subject Classification: 03F60, 47L50, 46S30

Keywords and Phrases: Constructive, operators, (ultra)weak operator topology, continuous functionals

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