1991 Fiscal Year Annual Research Report

作用素環における最近の話題の総合的研究

Research Project

Project/Area Number	02302004
Research Institution	Niigata University
Principal Investigator	斎藤吉助新潟大学, 理学部, 教授 (30018949)
Co-Investigator(Kenkyū-buntansha)	岸本晶孝北海道大学, 理学部, 教授 (00128597) 中神祥臣横浜市立大学, 文理学部, 教授 (70091246) 荒木不二洋京都大学, 数理解析研究所, 教授 (20027361) 富山淳東京都立大学, 理学部, 教授 (30006928) 境正一郎日本大学, 文理学部, 教授 (30130503)
Keywords	作用素環 / 無理数回転群 / 指数理論 / エルゴ-ト理論 / コンパクト作用素
Research Abstract	最近の数学は物理学、特に場の量子論と量子統計力学の影響を色濃く受けている。必然的に、量子力学の影響下に誕生した作用素環は数学の他の多くの分野と密接な関係を深めながら、その時代の大きな流れの中に新分野を開拓していった。例えば、非可換力学系、非可換微分幾何学、因子間の指数理論、量子群等多くのものがある。この様な訳で、作用素環の最近の話題は数多くあり、今後発展しそうな、または、新しく誕生しそうな分野等これから為すべき事が沢山ある。新潟大学で8月23日より24日の作用素環論研究集会を行った。この研究集会では9つの1時間講演を行ったが、奈良市のプレコングレスの影響があらゆる所に見受けられ、活発な質疑応答を行った。例えば、III型因子の部分因子環の構造について、指数理論とエルゴ-ド理論の関係、グラフ理論と因子環の指数の関係、無理数回転群とコンパクト作用素からなる環とのテンソル積上の自己同型写像について、作用素の不等式等話題が多く、多岐に渡っての講演が行われた。この研究集会で日本の若手研究者の活躍はめざましく、その影響は計り知れないものがある。今後の問題点や過去の結果についての検討などあらゆる角度から検討された。この研究による成果は今後の作用素環の理論の発展に大きく貢献するものと思える。

Research Products
(18 results)

All Other

All Publications (18 results)

[Publications] Marie Choda: "Duality for finite bipartite graph" Proc.Sattelite Conference of ICMー90. なし. 414-424 (1991)
[Publications] Marie Choda: "Entropy for canonical shifts II" Publ.RIMS Kyoto Univ.27. 461-489 (1991)
[Publications] KichiーSuke Saito: "Toeplitz operators associated with analytic crossed products II(invariant subspaces and factorization)" Integral Equation and Operator Theory. 14. 251-275 (1991)
[Publications] KichiーSuke Saito: "A simple approach to the invariant subspace structure of asnalytic crossed products" J.Operator Theory.
[Publications] KichiーSuke Saito: "The form of invariant subspaces of analytic crossed products" Proc.Sattelitite Conference of ICMー90. なし. 43-51 (1991)
[Publications] KichiーSuke saito: "An introduction to Toeplitz operators associated with analytic crossed crossed products" Contemporary Math.120. 165-168 (1991)
[Publications] D.E.Evans: "Compact group actions on UHF algebras obtained by folding the interval" J.Functional Analysis. 98. 346-360 (1991)
[Publications] Fumio Hiai: "Minimum index for subfactors and entropy II" J.Math.Soc.Japan. 43. 347-379 (1991)
[Publications] Fumio Hiai: "Closed convex hull of unitary orbits in von Neumann algebras" Trans Amer.Math.Soc.323. 1-38 (1991)
[Publications] KichiーSuke Saito: "On the angle operators between two projections in a von Neumann algebra" Archiv Math.
[Publications] Hideki Kosaki: "An inequality of ArakiーLiebーThirring(von Neumann algebra case)" Proc.Amer.Math.Soc.
[Publications] Yuji Konishi: "Some remarks on actions of compact matrix quantum groups on C*ーalgebras" Pacific J.Math.
[Publications] Tetsuya Masuda: "Representations of the quantum group SUq(2)and the little qーjacobi polynomials" J.Functional Analysis. 99. 357-386 (1991)
[Publications] Yoshihiro Nakamura: "The numerical index of nonselfadjoint operator algebras" Proc.Amer.Math.Soc.
[Publications] Kazuyuki Saito: "C*ーalgebras with countable and dense sets and tensor products of monotone complete C*ーalgebras" Quartly J.Math.
[Publications] Kazuyuki Saito: "All AW*ーalgebras are normal" J.London Math.Soc.
[Publications] Hujihiro Araki: "Current topics in operator algebras" World Scientific, 437 (1991)
[Publications] Shoichiro Sakai: "Operator algebras in dynamical systems" Cambridge Univ.Press, 219 (1991)

1991 Fiscal Year Annual Research Report

作用素環における最近の話題の総合的研究

Principal Investigator

斎藤 吉助 新潟大学, 理学部, 教授 (30018949)

Research Products

[Publications] Marie Choda: "Duality for finite bipartite graph" Proc.Sattelite Conference of ICMー90. なし. 414-424 (1991)

[Publications] Marie Choda: "Entropy for canonical shifts II" Publ.RIMS Kyoto Univ.27. 461-489 (1991)

[Publications] KichiーSuke Saito: "Toeplitz operators associated with analytic crossed products II(invariant subspaces and factorization)" Integral Equation and Operator Theory. 14. 251-275 (1991)

[Publications] KichiーSuke Saito: "A simple approach to the invariant subspace structure of asnalytic crossed products" J.Operator Theory.

[Publications] KichiーSuke Saito: "The form of invariant subspaces of analytic crossed products" Proc.Sattelitite Conference of ICMー90. なし. 43-51 (1991)

[Publications] KichiーSuke saito: "An introduction to Toeplitz operators associated with analytic crossed crossed products" Contemporary Math.120. 165-168 (1991)

[Publications] D.E.Evans: "Compact group actions on UHF algebras obtained by folding the interval" J.Functional Analysis. 98. 346-360 (1991)

[Publications] Fumio Hiai: "Minimum index for subfactors and entropy II" J.Math.Soc.Japan. 43. 347-379 (1991)

[Publications] Fumio Hiai: "Closed convex hull of unitary orbits in von Neumann algebras" Trans Amer.Math.Soc.323. 1-38 (1991)

[Publications] KichiーSuke Saito: "On the angle operators between two projections in a von Neumann algebra" Archiv Math.

[Publications] Hideki Kosaki: "An inequality of ArakiーLiebーThirring(von Neumann algebra case)" Proc.Amer.Math.Soc.

[Publications] Yuji Konishi: "Some remarks on actions of compact matrix quantum groups on C*ーalgebras" Pacific J.Math.

[Publications] Tetsuya Masuda: "Representations of the quantum group SUq(2)and the little qーjacobi polynomials" J.Functional Analysis. 99. 357-386 (1991)

[Publications] Yoshihiro Nakamura: "The numerical index of nonselfadjoint operator algebras" Proc.Amer.Math.Soc.

[Publications] Kazuyuki Saito: "C*ーalgebras with countable and dense sets and tensor products of monotone complete C*ーalgebras" Quartly J.Math.

[Publications] Kazuyuki Saito: "All AW*ーalgebras are normal" J.London Math.Soc.

[Publications] Hujihiro Araki: "Current topics in operator algebras" World Scientific, 437 (1991)

[Publications] Shoichiro Sakai: "Operator algebras in dynamical systems" Cambridge Univ.Press, 219 (1991)

斎藤吉助新潟大学, 理学部, 教授 (30018949)

[Publications] Kazuyuki Saito: "Cーalgebras with countable and dense sets and tensor products of monotone complete Cーalgebras" Quartly J.Math.