Study on preserver problems on Banach alebras
| Project/Area Number |
22540178
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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 | Niigata University |
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Principal Investigator |
HATORI Osamu 新潟大学, 自然科学系, 教授 (70156363)
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| Co-Investigator(Kenkyū-buntansha) |
MIURA Takeshi 山形大学, 理工学研究科, 教授 (90333989)
TAKAGI Hiroyuki 信州大学, 理学部, 教授 (20206725)
IZUCHI Keiji 新潟大学, 自然科学系, 教授 (80120963)
SAITO Kichisuke 新潟大学, 自然科学系, 教授 (30018949)
WATANABE Keiichi 新潟大学, 自然科学系, 准教授 (50210894)
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| Project Period (FY) |
2010 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2010: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | バナッハ環 / C*環 / 等距離写像 / 代数構造 / ユニタリー群 / 正値可逆元 / Thmpson距離 |
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| Research Abstract |
We give a structure theorem for isometries between the general linear groups of Banach algebras. As an application of it, we deduce the form of isometries between the general linear group of C*-algebras. We get a non-commutative Mazur-Ulam theorem and we describe the form of isometries between the full unitary group of a Hilbert space. We also get a result on the maps between certain commutative Banach algebras which preserve the norm non-symmetrically. We describe the form of the multiplicative isometries between F-algebras of holomorphic functions.
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Report
(4 results)
Research Products
(65 results)
