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On the infimum problem of Hilbert space effects
作者姓名:DU Hongke  DENG Chunyuan & LI Qihui College of Mathematics and Information Science  Shaanxi Normal University  Xi'an  China
作者单位:DU Hongke,DENG Chunyuan & LI Qihui College of Mathematics and Information Science,Shaanxi Normal University,Xi'an 710062,China
摘    要:The quantum effects for a physical system can be described by the set ε(H) of positive operators on a complex Hilbert space H that are bounded above by the identity operator I. The infimum problem of Hilbert space effects is to find under what condition the infimum A∧B exists for two quantum effects A and B∈ε(H). The problem has been studied in different contexts by R. Kadison, S. Gudder, M. Moreland, and T. Ando. In this note, using the method of the spectral theory of operators, we give a complete answer of the infimum problem. The characterizations of the existence of infimum A∧B for two effects A. B∈ε(H) are established.

收稿时间:25 February 2005
修稿时间:8 November 2005

On the infimum problem of Hilbert space effects
DU Hongke,DENG Chunyuan & LI Qihui College of Mathematics and Information Science,Shaanxi Normal University,Xi''''an ,China.On the infimum problem of Hilbert space effects[J].Science in China(Mathematics),2006,49(4):545-556.
Authors:DU Hongke  DENG Chunyuan  LI Qihui
Institution:College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, China
Abstract:The quantum effects for a physical system can be described by the set ɛ() of positive operators on a complex Hilbert space that are bounded above by the identity operator I. The infimum problem of Hilbert space effects is to find under what condition the infimum AB exists for two quantum effects A and B ε ɛ(). The problem has been studied in different contexts by R. Kadison, S. Gudder, M. Moreland, and T. Ando. In this note, using the method of the spectral theory of operators, we give a complete answer of the infimum problem. The characterizations of the existence of infimum AB for two effects A, B ε ɛ() are established.
Keywords:positive operator  quantum effect  infimum of quantum effects
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