Relative Hamiltonian for Faithful Normal States of a von Neumann Algebra | Zendy

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Relative Hamiltonian for Faithful Normal States of a von Neumann Algebra

Author(s) -

Huzihiro Araki

Publication year - 1973

Publication title -

publications of the research institute for mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.786

H-Index - 39

eISSN - 1663-4926

pISSN - 0034-5318

DOI - 10.2977/prims/1195192744

Subject(s) - mathematics , von neumann algebra , hamiltonian (control theory) , automorphism , combinatorics , operator (biology) , unitary operator , operator algebra , unitary state , discrete mathematics , pure mathematics , von neumann architecture , hilbert space , mathematical optimization , biochemistry , chemistry , repressor , political science , transcription factor , law , gene

Let W be a cyclic and separating vector for a von Neumann algebra 5ft and Jr be its modular operator. For any elements Qi,...,Qn in %R and complex numbers 2r lv.., zn such that Re Zj^>Q and I Re z^l/2, F is shown to be in the domain of A^Q,...A^Qn and \ApQi... A'w«QnV\^\Ql\...\Qn\\Vl A self adjoint operator h=h( ffl is called a Hamiltonian of a faithful normal state p of 9# relative to another faithful state 9) of %R if vectors £„ and £$ representing

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