Operator theory induced by operator inequalities

• Project/Area Number: 20540184
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Tohoku Pharmaceutical University
• Principal Investigator: TANAHASHI Kotaro 東北薬科大学, 薬学部, 教授 (90142398)
• Project Period (FY): 2008 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2011: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000); Fiscal Year 2010: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000); Fiscal Year 2009: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000); Fiscal Year 2008: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
• Keywords: ハイポノーマル作用素 / パラノーマル作用素 / クラスA作用素 / paranormal / k*-paranormal / m-isometry / SVEP / Bishop's property / 作用素不等式 / ビショップの性質ベータ / (p,k)-quasihyponormal作用素 / Fuglede-putnam定理 / ビショップの性質(ベータ) / p-hyponormal 作用素 / log-hyponormal 作用素

Research Abstract

We study structure and property of class A operators,(p, k)-quasihyponormal operators. Especially, we get a formulation for quasinilpotent part of these oprators and prove they enjoy the Fuglede-Putnam theorem and the Weyl's theorem under certain conditions.

Research Products

• [Journal Article] The single valued extension property for hereditarily normaloid operators (2012)
  • Author(s): 内山敦、棚橋浩太郎
  • Journal Title: Scientiae Mathematicae Japonicae Volume: e-2012 Pages: 57-60
  • NAID: 130007670114
  • Peer Reviewed
• [Journal Article] SVEP and Bishop's property for k*-paranormal operators and related topics (2012)
  • Author(s): 棚橋浩太郎、内山敦
  • Journal Title: 北海道大学講究録 Volume: 152 Pages: 31-41
• [Journal Article] Ulam type stability problems for alternative homomorphism (2012)
  • Author(s): 高橋眞映、三浦、高木、棚橋浩太郎
  • Journal Title: 北海道大学講究録 Volume: 152 Pages: 54-56
  • NAID: 120007101195
• [Journal Article] m-isometric operators (2012)
  • Author(s): 長宗雄、太田、棚橋浩太郎
  • Journal Title: 京都大学数理解析研究所講究録 Volume: 1778 Pages: 1-5
• [Journal Article] SVEP and Bishop's property for k*-paranormal operators and related topics (2012)
  • Author(s): 内山敦、棚橋浩太郎
  • Journal Title: 京都大学数理解析研究所講究録 Volume: 1778 Pages: 139-142
• [Journal Article] SVEP and Bishiop's property for k*-paranormal operators and related topics (2012)
  • Author(s): 棚橋浩太郎・内山敦
  • Journal Title: 北海道大学講究録 Volume: 152 Pages: 31-41
• [Journal Article] m-isometric operators (2012)
  • Author(s): 長宗雄・棚橋浩太郎
  • Journal Title: 数理解析研究所講究録 Volume: 1778 Pages: 1-5
• [Journal Article] *-paranormal operators and related topics (2012)
  • Author(s): 内山敦・棚橋浩太郎
  • Journal Title: 数理解析研究所講究録 Volume: 1778 Pages: 139-142
• [Journal Article] SVEP and Bishop's property beta for k*-paranormal operators (2011)
  • Author(s): N. M. Braha, 棚橋浩太郎
  • Journal Title: Operators and Matrices Volume: 5 Pages: 469-472
  • Peer Reviewed
• [Journal Article] SVEP and Bishop's property for k^*-paranormal operators (2011)
  • Author(s): N.L.Braha, K.Tanahashi
  • Journal Title: Operators and Matrices Volume: 5 Pages: 493-496
  • Peer Reviewed
• [Journal Article] On extension of some Fuglede-Putnam type theorems involving(p, k)-quasihyponormal (2009)
  • Author(s): 棚橋浩太郎, S. M. Patel, 内山敦
  • Journal Title: Mathematische Nachrichten Volume: 282 Pages: 1022-1032
  • Peer Reviewed
• [Journal Article] Weyl's type theorems for(p, k)-quasihyponormal operators (2009)
  • Author(s): S. Mecheri, 棚橋浩太郎, 内山敦
  • Journal Title: Scientiae Mathematicae Japonicae Volume: 69 Pages: 411-417
  • Peer Reviewed
• [Journal Article] Bishop's property(beta) for paranormal operators (2009)
  • Author(s): 内山敦、棚橋浩太郎
  • Journal Title: Operators and Matrices Volume: 3 Pages: 517-524
  • Peer Reviewed
• [Journal Article] On extension of some Fuglede-Putnam type theorems involving (p, k)-quasihyponormal, spectral, and dominant operators (2009)
  • Author(s): 棚橋浩太郎、S.M.Patel, 内山敦
  • Journal Title: Mathematische Nachrichten 282 Pages: 1022-1032
  • Peer Reviewed
• [Journal Article] Weyl's type theorems for (p, k)-quasihyponormal operators (2009)
  • Author(s): S.Mecheri, 棚橋浩太郎、内山敦
  • Journal Title: Scientiae Mathematicae Japonicae 69 Pages: 411-417
  • Peer Reviewed
• [Journal Article] Bishop's property (beta) for paranormal operators (2009)
  • Author(s): 内山敦、棚橋浩太郎
  • Journal Title: Operators and Matrices 3 Pages: 517-524
  • Peer Reviewed
• [Journal Article] On extensions of some Fuglede-Putnam type theorems involving (p, k)-quasihyponoirmal, spectral, and dominant operators (2009)
  • Author(s): K.Tanahashi, S.M.Patel A.Uchiyama
  • Journal Title: Mathematische Nachrichten 282 Pages: 1022-1032
  • Peer Reviewed
• [Journal Article] Bishop's property (beta) for paranormal operators (2009)
  • Author(s): A.Uchiyama, K.Tanahashi
  • Journal Title: Operators and Matrices 3 Pages: 517-524
  • Peer Reviewed
• [Journal Article] Weyl's type theorems for (p, k0-quasihyponormal operators (2009)
  • Author(s): S.Mecheri, K.Tanahashi, A.Uchiyama
  • Journal Title: Scientiae Mathematicae Japonicae 69 Pages: 411-417
  • Peer Reviewed
• [Journal Article] Quasinilpotent part of class A or(p, k)-quasihyponormal operators (2008)
  • Author(s): 棚橋浩太郎, I. H. Jeon, I. H. Kim, 内山敦
  • Journal Title: Operator Theory Volume: 187 Pages: 199-210
  • Peer Reviewed
• [Journal Article] Xia spectrum for some class of Operators (2008)
  • Author(s): 長宗雄、古谷正、棚橋浩太郎
  • Journal Title: Integral Equations and Operator Theory Volume: 61 Pages: 159-165
  • Peer Reviewed
• [Journal Article] Conditions implying self-adjointness of operators (2008)
  • Author(s): I. H. Jeon, I. H. Kim, 棚橋浩太郎、内山敦
  • Journal Title: Integral Equations and Operator Theory Volume: 61 Pages: 549-557
  • Peer Reviewed
• [Journal Article] Quasinilpotent part of class A or (p, k)-quasihyponormal operators (2008)
  • Author(s): 棚橋浩太郎、I.H.Jeon, I.H.Kim, 内山敦
  • Journal Title: Recent Advances in Operator Theory and Applications (Operator Theory : Advances and Applications) 187 Pages: 199-210
  • Peer Reviewed
• [Journal Article] Xia spectrum for some class of Operators (2008)
  • Author(s): 長宗雄、古谷正、棚橋浩太郎
  • Journal Title: Integral Equations and Operator Theory 61 Pages: 159-165
  • Peer Reviewed
• [Journal Article] Conditions implying self-adjointness of operators (2008)
  • Author(s): I.H.Jeon, I.H.Kim, 棚橋浩太郎、内山敦
  • Journal Title: Integral Equations and Operator Theory 61 Pages: 549-557
  • Peer Reviewed
• [Journal Article] Quasinilpotent part of class A or (p, k)-quasihyponormal operators (2008)
  • Author(s): K. Tanahashi, I. H. Jeon I. H. Kim, A. Uchiyama
  • Journal Title: Recent Advances in Operator Theory and Applications (Operator Theory : Advances and Applications) 187 Pages: 199-210
  • Peer Reviewed
• [Journal Article] Conditions implying self-adjointness of operators (2008)
  • Author(s): I. H. Jeon, I. H. Kim, K. Tanahashi, A. Uchiyama
  • Journal Title: Integral Equations and Operator Theory 61 Pages: 549-557
  • Peer Reviewed
• [Journal Article] Xia spectrum for some class of operators (2008)
  • Author(s): M. Cho, T. Huruya, K. Tanahashi
  • Journal Title: Integral Equations and Operator Theory 61 Pages: 159-165
  • Peer Reviewed
• [Presentation] SVEP and Bishiop's property for k*-paranormal operators and related topics (2011)
  • Author(s): 棚橋浩太郎・内山敦
  • Organizer: 第20回関数空間セミナー
  • Place of Presentation: 北海道大学
  • Year and Date: 2011-12-24
• [Presentation] Ulam type stability problems for alternative homomorphism (2011)
  • Author(s): 高橋・三浦・高木・棚橋
  • Organizer: 第20回関数空間セミナー
  • Place of Presentation: 北海道大学
  • Year and Date: 2011-12-24
• [Presentation] m-isometric operators (2011)
  • Author(s): 長宗雄・棚橋浩太郎
  • Organizer: スペクトル、数域などの作用素の幾何学的特性量を用いた作用素の構造研究
  • Place of Presentation: 京都大学
  • Year and Date: 2011-11-14
• [Presentation] *-paranormal operators and related topics (2011)
  • Author(s): 内山敦・棚橋浩太郎
  • Organizer: スペクトル、数域などの作用素の幾何学的特性量を用いた作用素の構造研究
  • Place of Presentation: 京都大学
  • Year and Date: 2011-11-14
• [Presentation] m-isometric operators,スペクトル (2011)
  • Author(s): 長宗雄、棚橋浩太郎
  • Organizer: 数域などの作用素の幾何学的特性量を用いた作用素の構造研究研究集会
  • Place of Presentation: 京都大学
• [Presentation] *-paranormal operators and related topics (2011)
  • Author(s): 内山敦、棚橋浩太郎
  • Organizer: スペクトル数域などの作用素の幾何学的特性量を用いた作用素の構造研究研究集会
  • Place of Presentation: 京都大学
• [Presentation] SVEP and Bishop's property for k*-paranormal operators and related topics (2011)
  • Author(s): 棚橋浩太郎、内山敦
  • Organizer: 第20回関数空間セミナー
  • Place of Presentation: 北海道大学
• [Presentation] Ulam type atability problems for alternative homomorphism (2011)
  • Author(s): 高橋眞映、三浦、高木、棚橋浩太郎
  • Organizer: 第20回関数空間セミナー
  • Place of Presentation: 北海道大学
• [Presentation] Spectral properties which imply Bishop's property (beta) (2009)
  • Author(s): A.Uchiyama, K.Tanahashi
  • Organizer: The 11th Kotac International Conference 2009
  • Place of Presentation: Daegu (Korea)
  • Year and Date: 2009-06-19
• [Presentation] Spectral properties which implies Bishop's property(beta) (2009)
  • Author(s): 内山敦、棚橋浩太郎
  • Organizer: Then 11^<th> Kotac International Conference 2009
  • Place of Presentation: 韓国テグ市
• [Presentation] Spectral properties which implies Bishop's property (beta) (2009)
  • Author(s): 内山敦、棚橋浩太郎
  • Organizer: Then 11^<th> Kotac International Conference 2009
  • Place of Presentation: 韓国テグ市
• [Presentation] An ordered pair of unitarily conjugate positive operators (Hyponormal operators) (2008)
  • Author(s): M. Takesaki, K. Tanahashi
  • Organizer: 作用素論・作用素環論研究集会
  • Place of Presentation: 大阪教育大学
  • Year and Date: 2008-11-20
• [Presentation] An ordered pair of unitarily conjugate positive operators(Hyponormal operators) (2008)
  • Author(s): 竹崎正道、棚橋浩太郎
  • Organizer: 作用素論・作用素環論研究集会
  • Place of Presentation: 大阪教育大学