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Zeno Product Formula Revisited |
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| Authors: | Pavel Exner Takashi Ichinose Hagen Neidhardt Valentin A Zagrebnov |
| Institution: | (1) Department of Theoretical Physics , NPI, Academy of Sciences, CZ-25068 Řež, Czech Republic;(2) Doppler Institute, Czech Technical University, Břehová 7, CZ-11519 Prague, Czech Republic;(3) Department of Mathematics, Faculty of Science, Kanazawa University, Kanazawa 920-1192, Japan;(4) WIAS Berlin, Mohrenstr. 39, D-10117 Berlin, Germany;(5) Départment de Physique, Université de la Méditerranée (Aix-Marseille II), F-13288 Marseille Cedex 9, France;(6) Centre de Physique Théorique Luminy, Case 907, F-13288 Marseille Cedex 9, France |
| 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. |
| Keywords: | Primary 47A55 47D03 81Q10 Secondary 47B25 |
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