Isometries of non-commutative Lp-spaces
1981 ◽
Vol 90
(1)
◽
pp. 41-50
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Keyword(s):
The spaces Lp(, φ) for 1 ≤ p ≤ ∞, where φ is a faithful semifinite normal trace on a von Neumann algebra , are defined in (10),(2),(14). The problem of determining the general form of an isometry of one such space into another has been studied in (i), (6), (9), (12), (5). Our main result, Theorem 2, is a characterization of such isometries for 1 ≤ p ≤ ∞, ≠ 2. The method of proof is based on that of (7), where isometries between Lp function spaces are characterized. The main step in the proof is Theorem 1, which gives the conditions under which equality holds in Clarkson's inequality.
1992 ◽
Vol 112
(3)
◽
pp. 575-579
◽
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
◽
1987 ◽
Vol 101
(2)
◽
pp. 363-373
◽
Keyword(s):
2007 ◽
Vol 1
(3)
◽
pp. 367-398
◽
1981 ◽
Vol 89
(3)
◽
pp. 405-411
◽
Keyword(s):
1969 ◽
Vol 9
(1-2)
◽
pp. 211-217
◽
Keyword(s):