Perturbations of the modular automorphism group |
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Authors: | Richard H Herman |
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Institution: | (1) University of California, Los Angeles, California;(2) Pennsylvania State University, State College, Pennsylvania |
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Abstract: | It is shown, under a necessary condition, that strong (pointwise) convergence of modular automorphism groups to a one parameter family of maps implies weak convergence of the respective states in the factor case. Moreover the limiting one parameter family of maps is the modular automorphism group for the limiting state. In the type I case weak convergence of the automorphism groups suffices. Norm convergence of the states is obtained in some cases. |
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