The positive contractive part of a noncommutative \(L^{p}\)-space is a complete Jordan invariant. (English) Zbl 1368.46050
R. V. Kadison [Ann. Math. (2) 56, 494–503 (1952; Zbl 0047.35703)] showed that several partial structures of a von Neumann algebra \(M\) can recover the von Neumann algebra up to Jordan \(*\)-isomorphisms. In this paper, the authors show that the positive part of the closed unit ball of a noncommutative \(L^p\)-space \((1\leq p\leq\infty)\), as a metric space, is a complete Jordan \(*\)-invariant for the underlying von Neumann algebra.
Reviewer: Ghadir Sadeghi (Sabzevār)
Keywords:
noncommutative \(L^p\)-spaces; positive contractive elements; metric spaces; bijective isometries; Jordan \({\ast}\)-isomorphismsCitations:
Zbl 0047.35703References:
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