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Proceedings of the American Mathematical Society

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Completely bounded linear extensions of operator-valued functions on $ \sp *$-semigroups


Author: Ching Yun Suen
Journal: Proc. Amer. Math. Soc. 105 (1989), 330-334
MSC: Primary 46L05; Secondary 47A20, 47D99
DOI: https://doi.org/10.1090/S0002-9939-1989-0931737-9
MathSciNet review: 931737
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Abstract: Let $ G$ be a unital $ *$-semigroup [7, p. 1] in a unital (complex) $ {C^*}$-algebra such that the linear span of $ G$ is norm dense in it. Extending the results of [6], we have completely bounded linear extension theorems of operatorvalued functions on $ G$. Applying extension theorems, we have that each regular bounded operator measure has the form $ V_1^*F(){V_2}$, where $ {V_1}$ and $ {V_2}$ are linear operators and $ F$ is a selfadjoint spectral operator measure.


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DOI: https://doi.org/10.1090/S0002-9939-1989-0931737-9
Keywords: $ *$-semigroup, $ M$-property, completely positive map, completely bounded map, operator measure
Article copyright: © Copyright 1989 American Mathematical Society