| Project/Area Number |
10640150
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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 | Yamagata University |
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Principal Investigator |
TAKAHASI Sin-ei Yamagata University Faculty of Enginnering Professor, 工学部, 教授 (50007762)
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| Co-Investigator(Kenkyū-buntansha) |
HATORI Osamu Niigata University Graduate School of Science and Technology Associate Professor, 大学院・自然科学研究科, 助教授 (70156363)
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| Project Period (FY) |
1998 – 2000
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| Project Status |
Completed (Fiscal Year 2000)
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| Budget Amount *help |
¥2,400,000 (Direct Cost: ¥2,400,000)
Fiscal Year 2000: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 1999: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1998: ¥1,100,000 (Direct Cost: ¥1,100,000)
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| Keywords | commutative Banach algebra / BSE-algbera / Segal algebra / Apostol algebra / Fourier multiplier algebra / Gelfand transform / bounded weaka approximate identity / Hlawka type inequalities / ring homomorphism / Hadamard product / Hlawka inequality / Djokovic inequality / Hyers-Ulam stability / locally compact Abeian group / cohomology / Fourier transform / natural spectra |
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| Research Abstract |
Classifications are based on setting several conditions and considering the classes to satisfy the conditions. This research has been focusing on clarifying the essence of commutative Banach algebras and Banach modules by the following idea : First, they would be classified according to the natural conditions settled, and then whether concrete algebras and modules belong to the classified groups or not, and what invariant properties the specific classified algebra and module have, might be investigated. Before this investigation, based on the above idea we have introduced and investigated the groups respective to BSE-algebras and BSE-Banach modules. In this research, a necessary and sufficient condition for a concrete Segal algebra on a locally compact abelian group to be BSE has been given. We further give a constraction of a minimal bounded weak approximate identities for these algebra. We also show that the greatest regular closed subalgebra and Apostol algebras of semisimple commutative Banach algebras are charaterized in terms of level sets of the maximal ideal spaces. Also the commutative Banach algebra of all Fourier multipliers on the Euclidian space which have have natural spectra has been investigated. Furthermore the relations between all measures with natural spectra on a compact abelian group and Apostol algebra has been considered and it is shown that both do not coincide with each other in the discrete case.
Finally, we have investigated a structure of ring-homomorphism on the unital semisimple commutative Banach algebras, a generalization of Mond-Pecauic's theorem on the converse of Jensen's inequality, Hadamard product versions of operator inequalities associated with extensions of Holder- McCarthy-Kantorovich inequality and Hlawka type inequalities on Banach spaces.
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