Crossed products of algebras of unbounded operators and structure of GW*-algebras

• Project/Area Number: 24540224
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Global analysis
• Research Institution: Fukuoka University
• Principal Investigator: INOUE ATSUSHI 福岡大学, 理学部, 非常勤講師 (50078557)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000); Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
• Keywords: 非有界＊-表現 / O*-代数 / 非可換微分構造 / 非有界＊-代数 / 非可換微分幾何 / 非有界*-代数 / C*-代数

Outline of Final Research Achievements

Inoue, M. Fragoulopoulou and K.D. Kuersten have defined and studied a GW*-crossed product of a GW*-algebra which is a natural generalization of a von Neumann algebra. Using the results, they have shown that a type III GW*-algebra is isomorphic to a GW*-crossed product of type II GW*-algebra under natural assumptions.

Research Products

• [Journal Article] Crossed products of algebras of unbounded operators. (2015)
  • Author(s): M. Fragoulopoulou, A. Inoue and K.-D. Kuersten
  • Journal Title: Banach J. Math. Anal. Volume: 9 Issue: 4 Pages: 316-358
  • DOI: 10.15352/bjma/09-4-16
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Tensor products of unbounded operator algebras (2014)
  • Author(s): M. Fragoulopoulou, A. Inoue and M. Weigt
  • Journal Title: Rocky Mountain J. Math. Volume: 44 Issue: 3 Pages: 895-912
  • DOI: 10.1216/rmj-2014-44-3-895
  • Peer Reviewed
• [Journal Article] Non-Self-Adjoint Resolutions of the Identity and Associated Operators (2014)
  • Author(s): A. Inoue and C. Trapani
  • Journal Title: Complex Analysis and Operator Theory Volume: 2014 Issue: 7 Pages: 1531-1546
  • DOI: 10.1007/s11785-014-0359-1
  • Peer Reviewed
• [Journal Article] Tensor products of generalized B*-algebras (2014)
  • Author(s): M. Fragoulopoulou, A. Inoue and M. Weigt
  • Journal Title: J. Math. Anal. Appl. Volume: 420 Issue: 2 Pages: 1787-1802
  • DOI: 10.1016/j.jmaa.2014.06.046
  • Peer Reviewed
• [Journal Article] Non-self-adjoint hamiltonians defined by Riesz bases (2014)
  • Author(s): F. Bagarello, A. Inoue and C. Trapani
  • Journal Title: J. Math. Phys. Volume: 55 Issue: 3 Pages: 1-12
  • DOI: 10.1063/1.4866779
  • Peer Reviewed
• [Journal Article] Weak commutation relations of unbounded operators : Nonlinear e (2012)
  • Author(s): F. Bagarello, A. Inoue and C. Trapani xtensions
  • Journal Title: J. Math. Phys. (2012) Volume: 53 Issue: 12
  • DOI: 10.1063/1.4764863
  • Peer Reviewed
• [Journal Article] Induced and reduced unbounded operator algebras (2012)
  • Author(s): F. Bagarello, A. Inoue and C. Trapani
  • Journal Title: Annali di Matematica Pura ed Applicata Volume: 191 Issue: 2 Pages: 285-292
  • DOI: 10.1007/s10231-010-0183-9
  • Peer Reviewed