Representable extensions of positive functionals and hermitian Banach -algebras

We present a general extension theorem for representable positive linear functionals defined on a * -subalgebra of an arbitrary * -algebra. The case of pure positive functionals is an improvement of the results from some previous works of Maltese [ 13 ], and Doran and Tiller [ 5 ]. From our statemen...

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Bibliographic Details
Published in:Acta mathematica Hungarica 2019-06, Vol.158 (1), p.66-86
Main Authors: Szűcs, Zs, Takács, B.
Format: Article
Language:English
Subjects:
Algebra
Group theory
Mathematics
Mathematics and Statistics
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Summary:We present a general extension theorem for representable positive linear functionals defined on a * -subalgebra of an arbitrary * -algebra. The case of pure positive functionals is an improvement of the results from some previous works of Maltese [ 13 ], and Doran and Tiller [ 5 ]. From our statement we obtain characterizations of hermitian Banach * -algebras, among others the classical ones. As applications we prove that H * -algebras and the L p -algebras of compact groups are hermitian.
ISSN:0236-5294
1588-2632
DOI:10.1007/s10474-018-00908-z