Abstract
Let\(\mathfrak{A}\) be aC*-algebra and\(\mathfrak{A}^ \circ \) be an opposite algebra. Notions of exact andj-positive states of\(\mathfrak{A}^ \circ \) ⊗\(\mathfrak{A}\) are introduced. It is shown, that any factor state ω of\(\mathfrak{A}\) can be extended to a pure exactj-positive state\(\tilde \omega \) of\(\mathfrak{A}^ \circ \) ⊗\(\mathfrak{A}\). The correspondence ω→\(\tilde \omega \) generalizes the notion of the purifications map introduced by Powers and Størmer. The factor states ω1 and ω2 are quasi-equivalent if and only if their purifications\(\tilde \omega _1 \) and\(\tilde \omega _2 \) are equivalent.
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Woronowicz, S.L. On the purification of factor states. Commun.Math. Phys. 28, 221–235 (1972). https://doi.org/10.1007/BF01645776
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DOI: https://doi.org/10.1007/BF01645776