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