Pavel Exner, Hagen Neidhardt, Takashi Ichinose, Valentin
Zeno product formula revisited
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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. [A revised version of mp_arc 04-379; to appear
in Integral Equation and Operator Theory.]