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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Central sequences associated with a state


Author: Sze Kai Tsui
Journal: Proc. Amer. Math. Soc. 82 (1981), 76-80
MSC: Primary 46L30
DOI: https://doi.org/10.1090/S0002-9939-1981-0603605-6
MathSciNet review: 603605
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Abstract: Central sequences associated with a state are defined and used to derive a characterization of the factor state in question. This characterization is used to study the factor state extension problem. One of the affirmative results obtained in this paper is as follows. Let $ \mathcal{A}_1$, be a finite dimensional sub-$ {C^ * }$*-algebra of $ \mathcal{A}$. Then every factor state on the relative commutant of $ \mathcal{A}_1$, in $ \mathcal{A}$ extends to a factor state on $ \mathcal{A}$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0603605-6
Keywords: Central sequences associated with a state, factor states, Kaplansky's density theorem, factor state extension, extreme points, projection mapping of norm one
Article copyright: © Copyright 1981 American Mathematical Society