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Representable extensions of positive functionals and hermitian Banach *-algebras

  • Zs. SzűcsEmail author
  • B. Takács
Article
  • 4 Downloads

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.

Key words and phrases

representable positive functional extension hermitian Banach *-algebra Lp-algebra of compact group 

Mathematics Subject Classification

primary 46L30 22D15 secondary 43A20 46K10 46K50 

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.Department of Differential EquationsBudapest University of Technology and EconomicsBudapestHungary
  2. 2.Department of MathematicsCorvinus University of BudapestBudapestHungary

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