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Absolutely Convergent Extensions of Nonclosable Positive Linear Functionals

Abstract

The existence of extensions of a positive linear functional ω defined on a dense *-subalgebra \({\mathfrak{A}_0}\) of a topological *-algebra \({\mathfrak{A}}\), satisfying certain regularity conditions, is examined. The main interest is focused on the case where ω is nonclosable and sufficient conditions for the existence of an absolutely convergent extension of ω are given.

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Correspondence to Camillo Trapani.

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Bellomonte, G., Trapani, C. & Triolo, S. Absolutely Convergent Extensions of Nonclosable Positive Linear Functionals. Mediterr. J. Math. 7, 63–74 (2010). https://doi.org/10.1007/s00009-010-0027-2

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Mathematics Subject Classification (2010)

  • 46H05

Keywords

  • Absolutely convergent extension
  • closable sesquilinear form