2010 Fiscal Year Final Research Report
Embedding of ordered normed spaces into numerical radius operator spaces
| Project/Area Number |
20540156
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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 | Gunma University |
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Principal Investigator |
ITOH Takashi Gunma University, 教育学部, 教授 (40193495)
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| Co-Investigator(Renkei-kenkyūsha) |
NAGISA Masaru 千葉大学, 理学部, 教授 (50189172)
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| Project Period (FY) |
2008 – 2010
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| Keywords | 作用素空間 / 数域半径作用素空間 / ノルム空間 / 完全有界性 / 完全正値性 / 行列作用素システム |
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| Research Abstract |
A normed space can be embedable into an operator space, which consists of operators on a Hilbert space. However, if the normed space has an order, it has not been obtained the embedding with preserving both norm and order. Then it is needed to study operators commuting with the embedding in order to hold the positivity. In this study, we determine the form of the maximal ideals in Toeplitz algebras whose generators commute with the embedding as the tensor form, by analyzing the multi-structure of upward-looking topology for Toeplitz algebras.
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