2006 Fiscal Year Final Research Report Summary
Studies of the structure of operators on analytic function spaces and their invariant subspaces
| Project/Area Number |
16340037
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 |
IZUCHI Keiji Niigata University, Institute of Science and Technology, Professor, 自然科学系, 教授 (80120963)
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| Co-Investigator(Kenkyū-buntansha) |
HATORI Osamu Niigata University, Institute of Science and Technology, Professor, 自然科学系, 教授 (70156363)
HURUYA Tadashi Niigata University, Institute of Social Science and Education, Professor, 教育科学系, 教授 (90018648)
NAKAZI Takahiko Hokkaido Univ., Graduate School of Science, Professor, 大学院理学研究科, 教授 (30002174)
HAYASHI Mikihiro Hokkaido Univ., Graduate School of Science, Professor, 大学院理学研究科, 教授 (40007828)
OHNO Syuichi Nippon Institute of Technology, Faculty of Technology, Associate Profesor, 工学部, 助教授 (20265367)
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| Project Period (FY) |
2004 – 2006
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| Keywords | analytic function space / invariant subspace / backward shift invariant subspace / Hardy space / bounded analytic functions / composition operator / singular inner function / commutative Banach algebra |
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| Research Abstract |
Izuchi (head of investigator) got the following results as the joint works.
1) Let M be an invariant subspace on the Hardy space over the bidisk. We have multiplication operators R_z and R_w on M. It is given a characterization of M for which rank[R_z, R*_w]=1. Also it is determined N=H^2Θ M satisfying rank[S_z, S*_w]=1.
2) It is given a lower and upper bound of the essential norms of the difference of composition operators on the space of bounded analytic functions H∞ on the open unit disk D. Also it is studied the topological structure of weighted composition operators on H∞.
3) It is studied quasi-invariant subspaces of the Fock space over C-2 generated by a polynomial.
4) It is given a characterization of two Hankel operators on H^2 for which their product is a compact perturbation of Hankel operator.
5) It is given a partial answer for Gorkin-Mortini' s problem on closed prime ideals of H∞.
6) It is studied a common zero set of equivalent singular inner functions in the maximal ideal space of H∞. Also it is solved two problems on singular inner functions posed by Mortini and Nicolau.
Nakazi (investigator) studied a commutant lifting theorem for compression operators.
Ohno (investigator) studied compact Hankel-type operators on the space of bounded harmonic functions h∞ on D. Also it is determined the essential norms of difference of composition operators on H∞.
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