Completely bounded linear extensions of operator-valued functions on -semigroups

Author:
Ching Yun Suen

Journal:
Proc. Amer. Math. Soc. **105** (1989), 330-334

MSC:
Primary 46L05; Secondary 47A20, 47D99

MathSciNet review:
931737

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a unital -semigroup [7, p. 1] in a unital (complex) -algebra such that the linear span of is norm dense in it. Extending the results of [6], we have completely bounded linear extension theorems of operatorvalued functions on . Applying extension theorems, we have that each regular bounded operator measure has the form , where and are linear operators and is a selfadjoint spectral operator measure.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1989-0931737-9

Keywords:
-semigroup,
-property,
completely positive map,
completely bounded map,
operator measure

Article copyright:
© Copyright 1989
American Mathematical Society