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

Abstract.

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 

Keywords.

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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