A Study of Embeddings of Normed Spaces into Numerical Radius Operator Spaces
| Project/Area Number |
18540159
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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, Education, Professor (40193495)
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| Co-Investigator(Kenkyū-buntansha) |
NAGISA Masaru Chiba University, Science, Professor (50189172)
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| Project Period (FY) |
2006 – 2007
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| Project Status |
Completed (Fiscal Year 2007)
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| Budget Amount *help |
¥1,020,000 (Direct Cost: ¥900,000、Indirect Cost: ¥120,000)
Fiscal Year 2007: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
Fiscal Year 2006: ¥500,000 (Direct Cost: ¥500,000)
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| Keywords | Operator Space / Numerical Radius / Operator Algebra / Onerator Norm / 数域半径作用素空間 |
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| Research Abstract |
In 1988, the notion of operator spaces introduced by Z.J.Ruan shed light on a new point of view for studying not only on operator algebra but also on functional analysis. We can introduce an operator space structure into the dual space of operator spaces and all of completely positive maps on operator spaces. It is not hard to transfer the arguments in normed spaces into those in operator spaces. As the catch phrase, it is said that " The operator space theory is a quantization of the functional analysis".
I and M.NGAISA proved the existence of various numerical radius operator spaces behind operator spaces. Given an operator space, we can find the various numerical radius norms which corresponds to the original norm satisfying an identity. We might say that " The numerical radius operator space theory is a second quantization of the functional analysis".
Moreover we found an-preserving representation of the involutive normed space into a concrete numerical radius operator space, while the Ruan's representation did not preserve the involution at all. As the consequence, we found the simple proof of Anto type theorem for numerical radius of operators, which describe the numerical radius by using the factorization of bounded operators on Hilbert spaces.
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Report
(3 results)
Research Products
(10 results)
