2000 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

Research Project

Project/Area Number	11640186
Research Institution	Science University of Tokyo
Principal Investigator	古田孝之東京理科大学, 理学部, 教授 (40007612)
Keywords	Lowner-Heinz inequality / Furuta inequality / generalized Furuta inequality / log majorization / order preserving inequality / chaotic order / relative operator entropy / positive definite operator
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)の定理は次のことである。A≧B≧0ならばA^p≧B^pただし1≧p≧0、しかしA≧B≧0であってもp>1に対しては必ずしもA^p≧B^pとは限らない。このため応用の上で大変不便であったので、それを解消するために我々はFuruta inequality(1987)を次のように確立した。【numerical formula】最近この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を次に述べてみよう。(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 inequ-ality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。最近Ando-Hiaiによるlog majorizationと同値な作用素不等式とFuruta inequalityを補間する作用素不等式のたった1頁の証明が得られた。

Research Products

(13 results)

All Other

All Publications (13 results)

[Publications] T.Furuta: "Generalized Furuta inequality in Banach *-algebra"Mathematical Inequalities and Applications. 2. 289-295 (1999)
[Publications] J.I.Fujii: "Simplified proof of characterization of chaotic order via Speditisno"Sciential Mathematical. 2. 63-64 (1999)
[Publications] T.Furuta: "On powers of p-hyponormal and log-hyponormal operators"J.Inequalities and Applications. 5. 367-380 (1999)
[Publications] T.Furuta: "On powers of p-hyponormal operators"Sciential Mathematical. 2. 279-284 (1999)
[Publications] T.Furuta: "An application of generalized Furuta inequality to Kanteron"Sciential Mathematical. 2. 393-399 (1999)
[Publications] T.Furuta: "Applications of Gramian transformation formula"Sciential Methematical. 3. 81-86 (1999)
[Publications] T.Furuta: "Simple proof of the concavity on operator entropy f(A)=-A lgA"Mathematical Inequalities and Applications. 3. 305-306 (1999)
[Publications] T.Furuta: "Results under logA【greater than or equal】logB can be derived from one…"Mathematical Inequalities and Applications. 3. 423-436 (2000)
[Publications] T.Furuta: "A folk theorem on Furuta inequality"Sciential Mathematical. 3. 229-231 (2000)
[Publications] T.Furuta: "The Holda McCarthy and Young inequalities on equivalent"American Mathematical Monthly. 106. 68-69 (2000)
[Publications] T.Furuta: "Spectral order A>B if and only if A^<2p-r>Z(A^<(-r)/2>B^pA^<(-r)/2>)(2p-r)/(p-r)…"Mathematical Inequalities and Applications. (to appear).
[Publications] T.Furuta: "Logarithmic order and dual logarithmic order"Acta Sci Math(Szeged). (to appear).
[Publications] T.Furuta: "A【greater than or equal】B【greater than or equal】O ensures (A^<r/2>A^pA^<r/2>)^<1/q>【greater than or equal】(A^<r/2>B^pA^<r/2>)^<1/q> for……"Math.Japonical. (to appear).

2000 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

Principal Investigator

古田 孝之 東京理科大学, 理学部, 教授 (40007612)

Research Products

[Publications] T.Furuta: "Generalized Furuta inequality in Banach *-algebra"Mathematical Inequalities and Applications. 2. 289-295 (1999)

[Publications] J.I.Fujii: "Simplified proof of characterization of chaotic order via Speditisno"Sciential Mathematical. 2. 63-64 (1999)

[Publications] T.Furuta: "On powers of p-hyponormal and log-hyponormal operators"J.Inequalities and Applications. 5. 367-380 (1999)

[Publications] T.Furuta: "On powers of p-hyponormal operators"Sciential Mathematical. 2. 279-284 (1999)

[Publications] T.Furuta: "An application of generalized Furuta inequality to Kanteron"Sciential Mathematical. 2. 393-399 (1999)

[Publications] T.Furuta: "Applications of Gramian transformation formula"Sciential Methematical. 3. 81-86 (1999)

[Publications] T.Furuta: "Simple proof of the concavity on operator entropy f(A)=-A lgA"Mathematical Inequalities and Applications. 3. 305-306 (1999)

[Publications] T.Furuta: "Results under logA【greater than or equal】logB can be derived from one…"Mathematical Inequalities and Applications. 3. 423-436 (2000)

[Publications] T.Furuta: "A folk theorem on Furuta inequality"Sciential Mathematical. 3. 229-231 (2000)

[Publications] T.Furuta: "The Holda McCarthy and Young inequalities on equivalent"American Mathematical Monthly. 106. 68-69 (2000)

[Publications] T.Furuta: "Spectral order A>B if and only if A^<2p-r>Z(A^<(-r)/2>B^pA^<(-r)/2>)(2p-r)/(p-r)…"Mathematical Inequalities and Applications. (to appear).

[Publications] T.Furuta: "Logarithmic order and dual logarithmic order"Acta Sci Math(Szeged). (to appear).

[Publications] T.Furuta: "A【greater than or equal】B【greater than or equal】O ensures (A^<r/2>A^pA^<r/2>)^<1/q>【greater than or equal】(A^<r/2>B^pA^<r/2>)^<1/q> for……"Math.Japonical. (to appear).

古田孝之東京理科大学, 理学部, 教授 (40007612)