Non Commutative Lp Spaces II
1982 ◽
Vol 34
(5)
◽
pp. 1208-1214
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Keyword(s):
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
1981 ◽
Vol 33
(6)
◽
pp. 1319-1327
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1978 ◽
Vol 84
(1)
◽
pp. 47-56
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Keyword(s):
2004 ◽
Vol 56
(5)
◽
pp. 983-1021
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Keyword(s):
1979 ◽
Vol 31
(5)
◽
pp. 1012-1016
◽
Keyword(s):
1999 ◽
Vol 02
(01)
◽
pp. 169-178
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Keyword(s):
2002 ◽
Vol 132
(1)
◽
pp. 137-154
◽
2005 ◽
Vol 08
(02)
◽
pp. 215-233
◽