Functional analytic study on infinite dimensional groups

• Project/Area Number: 26800055
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Basic analysis
• Research Institution: Shinshu University
• Principal Investigator: Matsuzawa Yasumichi 信州大学, 学術研究院教育学系, 助教 (60645620)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Project Status: Completed (Fiscal Year 2017)
• Budget Amount: ¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000); Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
• Keywords: 無限次元群 / ユニタリ群 / 自己共役作用素 / 同値関係 / 記述集合論 / Weyl-von Neumann同値 / von Neumann環 / ハイパー群 / ワイル・フォンノイマン同値関係 / 非有界作用素 / Hilbert空間

Outline of Final Research Achievements

(1) We studied the unitary equivalence relation modulo the compacts for self-adjoint operators from a descriptive set theoretical point of view. It was shown that this equivalence relation cannot be classified by countable structures.
(2) We studied topological groups which can be embedded into the unitary group of a finite von Neumann algebra. Such groups are called finite type groups. Finite type groups admit a compatible bi-invariant metric and can be embedded into the unitary group on a Hilbert space. It was shown that these two conditions are not sufficient to be a finite type group.

Research Products

• [Int'l Joint Research] ドレスデン工科大学(ドイツ)
• [Int'l Joint Research] ドレスデン工科大学(ドイツ)
• [Int'l Joint Research] コペンハーゲン大学(デンマーク)
• [Journal Article] Non-commutative hypergroup of order five (2017)
  • Author(s): Yasumichi Matsuzawa, Hiromichi Ohno, Akito Suzuki, Tatsuya Tsurii, Satoe Yamanaka
  • Journal Title: Journal of Algebra and Applications Volume: 印刷中 Issue: 07 Pages: 1750127-1750127
  • DOI: 10.1142/s0219498817501274
  • NAID: 120007100052
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] When does the Weyl-von Neumann Theorem hold? (2017)
  • Author(s): Ando Hiroshi、Matsuzawa Yasumichi
  • Journal Title: Bulletin of the London Mathematical Society Volume: 49 Issue: 4 Pages: 742-744
  • DOI: 10.1112/blms.12064
  • Peer Reviewed
• [Journal Article] Unitarizability, Maurey-Nikishin factorization, and Polish groups of finite type (2017)
  • Author(s): Ando Hiroshi、Matsuzawa Yasumichi、Thom Andreas、Tornquist Asger
  • Journal Title: Journal fur die reine und angewandte Mathematik (Crelles Journal) Volume: 0 Issue: 758 Pages: 223-251
  • DOI: 10.1515/crelle-2017-0047
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] The Weyl-von Neumann Theorem and Borel Complexity of Unitary Equivalence Modulo Compacts of Self-Adjoint Operators (2015)
  • Author(s): Hiroshi ANDO and Yasumichi MATSUZAWA
  • Journal Title: The Royal Society of Edinburgh Proceedings A (Mathematics) Volume: 145 Issue: 6 Pages: 1115-1144
  • DOI: 10.1017/s0308210515000293
  • NAID: 120006459742
  • Peer Reviewed
• [Journal Article] On Borel equivalence relations related to self-adjoint operators (2015)
  • Author(s): Hiroshi ANDO and Yasumichi MATSUZAWA
  • Journal Title: Journal of Operator Theory Volume: 74 Issue: 1 Pages: 183-194
  • DOI: 10.7900/jot.2014may24.2030
  • Peer Reviewed / Acknowledgement Compliant
• [Presentation] Groups of unitaries without property (FH) (2017)
  • Author(s): 松澤泰道
  • Organizer: 日本数学会
  • Place of Presentation: 首都大学東京
  • Year and Date: 2017-03-26
• [Presentation] 群の従順性とユニタリ化可能性 (2017)
  • Author(s): 松澤泰道
  • Organizer: 今野・竹居研究室セミナー
  • Invited
• [Presentation] 無限次元群の話 (2015)
  • Author(s): 松澤泰道
  • Organizer: 作用素論作用素環論研究集会
  • Place of Presentation: KKR妙高高原白樺荘（新潟県妙高市）
  • Year and Date: 2015-10-25
  • Invited
• [Presentation] Weyl-von Neumann同値関係の複雑さ (2015)
  • Author(s): 松澤泰道
  • Organizer: 日本数学会年会
  • Place of Presentation: 明治大学
  • Year and Date: 2015-03-22
• [Presentation] 量子力学に於ける時間作用素について (2014)
  • Author(s): 松澤泰道
  • Organizer: Nagahama Workshop "From Quantum to Life"
  • Place of Presentation: 長浜バイオ大学
  • Year and Date: 2014-11-15
  • Invited
• [Presentation] Weyl-von Neumannの定理の複雑さ (2014)
  • Author(s): 松澤泰道
  • Organizer: 量子場の数理とその周辺（RIMS研究集会）
  • Place of Presentation: 京都大学
  • Year and Date: 2014-10-06
  • Invited
• [Presentation] Hilbert-Schmidt群のFock空間上での表現 (2014)
  • Author(s): 松澤泰道
  • Organizer: 札幌数理物理研究集会
  • Place of Presentation: 北海道大学
  • Year and Date: 2014-09-01
  • Invited
• [Remarks] 松澤泰道のホームページ
  • URL: https://sites.google.com/site/yasumichimatsuzawa/jp