2013 Fiscal Year Final Research Report
Quasi-diagonality and approximate innerness of flows on C*-algebras
| Project/Area Number |
23540229
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Hokkaido University |
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Principal Investigator |
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| Project Period (FY) |
2011 – 2013
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| Keywords | 作用素環 / Cスター環 / 流れ / 内部近似性 / 準対角性 |
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| Research Abstract |
von Neumann successfully placed the theory of operators on Hilbert space in the foundation of quantum mechanics. He later developed the theory of operator rings (or algebras), probably thought of as a foundation of quantum mechanics of infinite degree of freedom such as quantum field theory, but he never completed that project by being distracted by other callings. Around the ending of WWII Gel'fand, Naimark and Segal initiated the theory of C*-algebras and asserted it was the scheme we were after as a framework of quantum physics of infinite degrees of freedom. This project was built up on this claim and was to investigate flows on C*-algebras as appearing as time-developments. We established many properties of approximately inner flows which were supposed to appear in physical models, and quas-diagonal flows, which include the formers and look more amenable.
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