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Characterization of Normal Traces on Von Neumann Algebras by Inequalities for the Modulus |
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| Authors: | Stolyarov A. I. Tikhonov O. E. Sherstnev A. N. |
| Affiliation: | (1) Kazan State University, Russia |
| Abstract: | It is proved that if a normal semifinite weight  on a von Neumann algebra  satisfies the inequality  for any selfadjoint operators  in  , then this weight is a trace. Several similar characterizations of traces among the normal semifinite weights are proved. In particular, Gardner's result on the characterization of traces by the inequality  is refined and reinforced. |
| Keywords: | von Neumann algebra normal semifinite weight trace ultrastrong topology ultraweak topology |
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