1999 Fiscal Year Annual Research Report
コンピュータを活用した作用素不等式の開発とその応用
| Project/Area Number |
11640186
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| Research Institution | Tokyo University of Science |
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Principal Investigator |
古田 孝之 東京理科大学, 理学部, 教授 (40007612)
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| Keywords | Lowner-Heinz不等式 / Furuta inequality / relative entropy / order preserving inequality / chaotic order / log-hyponormal / p-hyponormal / Kantorovich inequality |
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| Research Abstract |
ヒルベルト空間上の有界線形作用素の順序保存に関する有名なLowner-Heinz(1934)の定理の応用の上の不便さを解消するために我々はFuruta inequality(1987)を次のように確立した。
Furuta inequality"A【greater than or equal】B【greater than or equal】0 ensuresA^<(p+r)/q>【greater than or equal】(A^<r/2>B^pA^<r/2>)^<1/q>holds for any p【greater than or equal】0,r【greater than or equal】0 and q【greater than or equal】1with(1+r)q【greater than or equal】p+r."
Furuta inequalityの応用が多方面において見つかっている。それは主に次の三分野においてである。(a)作用素不等式、(b)ノルム不等式、(c)作用素方程式。これらの応用のうち主なものは(a_1)relative operator entoropyへの応用(a_2)Ando-Hiaiのlog majorizationへの応用(a_3)Generalized Aluthge transformation(b_1)Heinz-Kato inequalityの一般化(b_2)Kosaki trace inequalityの一般化(c_1)Pedersen-Takesakiの作用素方程式の一般化などである。今回(a_3)p-hyponormal作用素やlog-hyponormal作用素への応用が得られた。(b_3)Kantorovich型不等式への一般化されたFuruta inequalityの応用でchaotic orderの特徴付けが得られた。
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Research Products
(11 results)
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[Publications] Takayuki Furuta: "Simple proof of the concairty on operator entropy f(A)=-A log A"Mathematical Inequalities&Applications. 2(in press). (2000)
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[Publications] M.Fujiii,T.Furuta&R.Nakamoto: "Applications of Gramian transformation formula"Scientiae Mathematical. (in press). (2000)
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[Publications] T.Furuta&Y.Seg: "An application of generalized Furuta inequality to Kantorovich・・・・"Scientiae Mathematical. 2. 393-399 (1999)
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[Publications] T.Furuta&M.Yanagida: "On powers of p-hyponormal operators"Scientiae Mathematical. 2. 279-284 (1999)
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[Publications] T.Furuta&M.Yanagida: "On powers of p-hyponormal and log-haiponormal operators"J.Inequalities&Applications. (in press). (1999)
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[Publications] J.I.Fujii,T.Furuta,T.Yamazaki&M.Yanagida: "Simplified proof of characterization of chaotic order・・・・"Scientiae Mathematical. 2. 63-64 (1999)
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[Publications] Takayuki Furuta: "Generalized Furuta inequality in Banach*-algebra"Mathematical Inequalities&Applications. 2. 289-295 (1999)
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[Publications] T.Furuta,M.Ito&T.Yamazaki: "A subclass of paranormal operators including・・・・"Scientiae Mathematical. 3. 389-403 (1998)
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[Publications] T.Furuta,T.Yamazaki&M.Yanagida: "Order preserving operator function via Furuta inequality"Proceedings of 96-IWOTA. 1. 175-184 (1998)
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[Publications] T.Furuta&M.Yanagida: "Generalized means and convexity of inversion for positive operators"American Mathematical Monthly. 105. 258-259 (1998)
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[Publications] (]SY.gtoreq. 〔o ensures (a┣dl┣d7r(/)2┫d7┫dla┣dlp┫dla┣dl┣d7r(/)2┫d7┫dl)┣dl┣d7l(/)q┫d7┫dl(〕sy.gtoreq.(A^<1/2>B^pA^<r/2>)^<1/q> for・・・・"Kluwer Academic Publishers. 20 (1999)
