Abstract
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 Lp-algebras of compact groups are hermitian.
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Szűcs, Z., Takács, B. Representable extensions of positive functionals and hermitian Banach *-algebras. Acta Math. Hungar. 158, 66–86 (2019). https://doi.org/10.1007/s10474-018-00908-z
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DOI: https://doi.org/10.1007/s10474-018-00908-z