The Haagerup problem on subadditive weights on W*-algebras. II |
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Authors: | A M Bikchentaev |
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Institution: | 1. Kazan (Volga Region) Federal University, ul. Kremlyovskaya 18, Kazan, 420008, Russia
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Abstract: | In 1975 U. Haagerup has posed the following question: Whether every normal subadditive weight on a W*-algebra is σ-weakly lower semicontinuous? In 2011 the author has positively answered this question in the particular case of abelian W*-algebras and has presented a general form of normal subadditive weights on these algebras. Here we positively answer this question in the case of finite-dimensional W*-algebras. As a corollary, we give a positive answer for subadditive weights with some natural additional condition on atomic W*-algebras. We also obtain the general form of such normal subadditive weights and norms for wide class of normed solid spaces on atomic W*-algebras. |
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