WIAS Preprint No. 1053, (2005)

Zeno product formula revisited


  • Exner, Pavel
  • Ichinose, Takashi
  • Neidhardt, Hagen
  • Zagrebnov, Valentin

2010 Mathematics Subject Classification

  • 47A55 47B25 47D03 81Q10


  • Zeno dynamics, product formulæ, resolvents, convergence, generalized observables




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.

Appeared in

  • Integral Equations Operator Theory, 57 (2007) pp. 67--81.

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