Integral Equations and Operator Theory

, Volume 57, Issue 1, pp 67–81 | Cite as

Zeno Product Formula Revisited

  • Pavel Exner
  • Takashi Ichinose
  • Hagen Neidhardt
  • Valentin A. Zagrebnov
Article

Abstract.

We introduce a new product formula which combines an orthogonal projection with a complex function of a non-negative operator. Under certain assumptions on the complex function the strong convergence of the product formula is shown. Under more restrictive assumptions even operator-norm convergence is verified. The mentioned formula can be used to describe Zeno dynamics in the situation when the usual non-decay measurement is replaced by a particular generalized observables in the sense of Davies.

Mathematics Subject Classification (2000).

Primary 47A55 47D03 81Q10 Secondary 47B25 

Keywords.

Zeno dynamics product formulæ resolvents convergence generalized observables 

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Copyright information

© Birkhäuser Verlag, Basel/Switzerland 2006

Authors and Affiliations

  • Pavel Exner
    • 1
    • 2
  • Takashi Ichinose
    • 3
  • Hagen Neidhardt
    • 4
  • Valentin A. Zagrebnov
    • 5
    • 6
  1. 1.Department of Theoretical Physics , NPIAcademy of SciencesŘežCzech Republic
  2. 2.Doppler InstituteCzech Technical UniversityPragueCzech Republic
  3. 3.Department of Mathematics, Faculty of ScienceKanazawa UniversityKanazawaJapan
  4. 4.WIAS BerlinBerlinGermany
  5. 5.Départment de PhysiqueUniversité de la Méditerranée (Aix-Marseille II)Marseille Cedex 9France
  6. 6.Centre de Physique Théorique Luminy, Case 907Marseille Cedex 9France

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