Integral Equations and Operator Theory

, Volume 50, Issue 1, pp 57–81

Extension of Locally Defined Indefinite Functions on Ordered Groups

Original paper

DOI: 10.1007/s00020-003-1223-2

Cite this article as:
Bruzual, R. & Domínguez, M. Integr. equ. oper. theory (2004) 50: 57. doi:10.1007/s00020-003-1223-2


We give a definition of κ-indefinite function of archimedean type, on an interval of an ordered group Ω with an archimedean point. We say that Ω has the indefinite extension property if every continuous κ-indefinite function of archimedean type, on an interval of Ω, can be extended to a continuous κ-indefinite function on the whole group Ω.

We show that if a group Γ is semi-archimedean and it has the indefinite extension property, then \(\Gamma \times \mathbb{Z}\) with the lexicographic order and the product topology has the indefinite extension property. As a corollary it is obtained that the groups \(\mathbb{Z}^n \) and \(\mathbb{R} \times \mathbb{Z}^n ,\) with the lexicographic order and the usual topologies, have the indefinite extension property.

Mathematics Subject Classification (2000).

Primary 47B50 Secondary 46C20, 47D03 


Indefinite metric spaces operator valued indefinite functions semi-group of operators lexicographic order 

Copyright information

© Birkhäuser Verlag, Basel 2004

Authors and Affiliations

  1. 1.Escuela de Matemática, Fac. CienciasUniversidad Central de VenezuelaVenezuela
  2. 2.CaracasVenezuela
  3. 3.CaracasVenezuela

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