Geodesic
Non Commutative Lp Spaces II
Canadian journal of mathematics, Tome 34 (1982) no. 5, pp. 1208-1214

Voir la notice de l'article provenant de la source Cambridge University Press

Let M be a w*-algebra (Von Neumann algebra), τ a semifinite, faithful, normal trace on M. There exists a w*-dense (i.e., dense in the σ(M, M *)-topology, where M * is the predual of M) *-ideal J of M such that τ is a linear functional on J, and (where |x| = (x*x)1/2) is a norm on J. The completion of J in this norm is Lp (M, τ) (see [2], [8], [7], and [4]).If M is abelian, in which case there exists a measure space (X, μ) such that M = L ∞(X, μ), then Lp (X, τ) is isometric, in a natural way, to Lp (X, μ). A natural question to ask is whether this situation persists if M is non-abelian. In a previous paper [5] it was shown that it is not possible to have a linear mapping 
Katavolos, A. Non Commutative Lp Spaces II. Canadian journal of mathematics, Tome 34 (1982) no. 5, pp. 1208-1214. doi: 10.4153/CJM-1982-083-8
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