Study on operator theory and operator means

算子理论及算子手段研究

• 批准号: 19340035
• 负责人: KOSAKI Hideki
• 金额: $ 8.32万
• 依托单位: Kyushu University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2007
• 资助国家: 日本
• 起止时间: 2007 至 2010
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-19340035/
• 关键词: 作用素平均; 正定値関数; ノルム不等式; ユニタリ不変ノルム; Jensen型不等式; majorization理論; 因子環; 無限分割可能行列; 作用素凹関数

Operator means can be constructed from certain scalar means in a natural fashion, and comparison of unitarily invariant norms of such operator means requires positive definiteness of ratios of corresponding scalar means. Positive definiteness for many such ratios was determined, and consequently many very precise norm inequalities (such as an abundance of generalizations of the Heinz inequality and monotonicity in a parameter of norms of operator binomial means) were obtained. Moreover, many such positive definite functions arising in this way were shown to be infinitely divisible. Also, Jensen-type majorization results and the equality condition for the trace Jensen inequality were proved in the setting of von Neumann algebras.

算符平均可以由一定的标量平均以自然的方式构造，而这种算符平均的么正不变范数的比较需要相应的标量平均的比率的正定性。确定了许多这类比率的正定性，从而得到了许多非常精确的范数不等式(如Heinz不等式的大量推广和算子二项平均范数参数的单调性)。此外，许多以这种方式产生的正定函数被证明是无穷可除的。在von Neumann代数的背景下，证明了Jensen型优超结果和迹Jensen不等式的等价条件。

项目成果

On operator means

操作员手段

• 发表时间: 2010
• 作者: 江渝;中村玄;藤原宏志;H.Kosaki
• 通讯作者: H.Kosaki

Trace Jensen inequality and related weak majorizationin semi-finite von Neumann algebra

半有限冯诺依曼代数中的追踪詹森不等式和相关的弱多数化

• 期刊: J.Operator Theory (to appear)
• 作者: T. Harada;H. Kosaki
• 通讯作者: H. Kosaki

Toeplitz-composition C^*-algebras for certain finite Blaschke products

某些有限 Blaschke 产品的 Toeplitz 组合 C^* 代数

• 发表时间: 2010
• 期刊: Proc.Amer.Math.Soc.
• 作者: H.Hamada;Y.Watatani
• 通讯作者: Y.Watatani

Trace Jensen type inequality in von Neumann algebras and related topics

冯诺依曼代数及相关主题中的迹 Jensen 型不等式

• 发表时间: 2008
• 作者: 中村玄;江渝;永安聖;程晋;H.Kosaki
• 通讯作者: H.Kosaki

On Jensen-type majorizations in semifinite von Neumann algebras, Noncommutative Lp-spaces

关于半有限冯诺依曼代数中的 Jensen 型大化，非交换 Lp 空间

• 发表时间: 2007
• 作者: 中村玄;江渝;永安聖;程晋;H.Kosaki;H. Kosaki
• 通讯作者: H. Kosaki