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Index Theory for Toeplitz Operators on Algebraic Spaces
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| 자료유형 | 학위논문 |
|---|---|
| 서명/저자사항 | Index Theory for Toeplitz Operators on Algebraic Spaces. |
| 개인저자 | Jabbari, Mohammad. |
| 단체저자명 | Washington University in St. Louis. Mathematics. |
| 발행사항 | [S.l.]: Washington University in St. Louis., 2019. |
| 발행사항 | Ann Arbor: ProQuest Dissertations & Theses, 2019. |
| 형태사항 | 91 p. |
| 기본자료 저록 | Dissertations Abstracts International 81-05B. Dissertation Abstract International |
| ISBN | 9781088392645 |
| 학위논문주기 | Thesis (Ph.D.)--Washington University in St. Louis, 2019. |
| 일반주기 |
Source: Dissertations Abstracts International, Volume: 81-05, Section: B.
Advisor: Tang, Xiang. |
| 이용제한사항 | This item must not be sold to any third party vendors. |
| 요약 | This dissertation is about the abstract Toeplitz operators obtained by compressing the multishifts of the usual Hilbert spaces of analytic functions onto co-invariant subspaces generated by polynomial functions. These operators were introduced by Arveson in regard to his multivariate dilation theory for spherical contractions. The main technical issue here is essential normality, addressed in Arveson's conjecture. If this conjecture holds true then the fundamental tuple of Toeplitz operators associated to a polynomial ideal I can be thought as noncommutative coordinate functions on the variety defined by I intersected with the boundary of the unit ball. This interpretation suggests operator-theoretic techniques to study certain algebraic spaces. More specifically, we are interested in Douglas' index problem. In the special case of monomial ideals we give a new proof for Arveson's essential normality conjecture, also answer Douglas' index problem. Our main construction is a certain resolution (in the sense of homological algebra) of Hilbert modules. Finally, Thinking of the fundamental tuple of Toeplitz operators as noncommutative coordinate functions, we start applying them to study the isolated singularities of algebraic hypersurfaces. The main extra operator-theoretic ingredient here is a unitary operator, the holonomy of a certain Gauss-Manin connection induced by the monodromy of the singularity. We want to understand how this unitary operator interacts with the Toeplitz operators. This study could lead to an analytic way for detecting exotic smooth structures on odd-dimensional spheres. |
| 일반주제명 | Mathematics. |
| 언어 | 영어 |
| 바로가기 | 
: 이 자료의 원문은 한국교육학술정보원에서 제공합니다. |
