2011 Fiscal Year Final Research Report
The construction ofthe spectral theory on quantum deformed operators and its application to quantum physics
| Project/Area Number |
20540178
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Kyushu University |
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Principal Investigator |
OTA Shoichi 九州大学, 大学院・芸術工学研究院, 教授 (70107176)
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| Co-Investigator(Renkei-kenkyūsha) |
INOUE Atushi 福岡大学, 理学部, 教授 (50078557)
CHO Muneo 神奈川大学, 工学部, 教授 (10091620)
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| Project Period (FY) |
2008 – 2011
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| Keywords | unbounded operator / deformed operator / q-normal operator / Hilbert space / subnormal operator |
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| Research Abstract |
A kind of spectral theory of q-deformed operators in a Hilbert space is needed so that unbounded representations of quantum algebras are analyzed. This work is devoted toinvestigating a q-normal operator in a Hilbert space, compared with a standard spectral measure and the spectral decomposition for a normal operator in a Hilbertspace. It is shown that, if a positive number q is smaller than 1, every q-normal operator in a Hilbert space is extended to a standard normal operator in a possibly larger Hilbert space.
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