Research on Inclusion Relations of Subalgebras
子代数包含关系研究
基本信息
- 批准号:03640156
- 负责人:
- 金额:$ 1.09万
- 依托单位:
- 依托单位国家:日本
- 项目类别:Grant-in-Aid for General Scientific Research (C)
- 财政年份:1991
- 资助国家:日本
- 起止时间:1991 至 1992
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
In a field of operator algebras, we studied global analysis of inclusion relations of von Neumann subalgebras. We have made it clear what played principal roles on the analysis and have established some reduction theory to irreducible inclusion relations.In order to do so, first of all, we defined some types of inclusion relations, so called, semifinite type and finite type. Secondly, we developed some new notions and their properties on Radon-Nikodym derivative and disintegration of operator valued weights. For an operator valued weight E from a von Neumann algebra onto a subalgebra, we define the standard correspondent (or commutant) E' of E, which satisfies a chain rule property. Applying these results, we can get the following. (1) A chain rule property is also true to hold for indicial derivative of an operator valued weight, whose notion had been developed by us. (2) For a general pair of von Neumann algebras, if there is a conditional expectation whose index is a bounded operator, there exists uniquely the conditional expectation of minimal index type. This is an extension of Hiai's result. (3) It is easy to show that a convolution of conditional expectations of minimal type is also of minimal type in a general setting. (4) For a problem on additivity of Pimsner-Popa's entropy, we have succeeded to give a complete answer.In a field of function algebra, we have made clear some relation among a zero set, a peak interpolation set, and so on for an analytic function algebra.
在算子代数领域,我们研究了冯诺依曼子代数包含关系的全局分析。我们明确了什么在分析中起主要作用,并建立了一些不可约包含关系的约简理论。为此,我们首先定义了一些类型的包含关系,即所谓的半有限型和有限型。其次,我们提出了一些关于 Radon-Nikodym 导数和算子值权值分解的新概念及其性质。对于从冯·诺依曼代数到子代数的算子赋值权重 E,我们定义 E 的标准对应(或交换)E',它满足链式法则属性。应用这些结果,我们可以得到以下结果。 (1) 链式法则性质也适用于算子估值权重的指数导数,其概念是我们提出的。 (2) 对于一般的冯·诺依曼代数对,如果存在索引为有界算子的条件期望,则唯一存在最小索引类型的条件期望。这是Hiai结果的延伸。 (3) 很容易证明最小类型的条件期望的卷积在一般情况下也是最小类型的。 (4) 对于一个关于Pimsner-Popa熵的可加性问题,我们成功地给出了完整的答案。在函数代数领域,我们明确了零集、峰值插值集等之间的一些关系:解析函数代数。
项目成果
期刊论文数量(2)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
市原 亮(河上 哲): "Radon-Nikodym derivative for operator valued weights" Bull.Nara Univ.Educ.40. 1-7 (1991)
Ryo Ichihara (Satoshi Kawakami):“算子值权重的 Radon-Nikodym 导数”Bull.Nara Univ.Educ.40 (1991)。
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:
- 通讯作者:
Ryo Ichihara: "RadonーNikodym Derivative for Operator Valued Weights" Bulletin of Nara University of Education. 40. 1-7 (1991)
Ryo Ichihara:“算子值权重的 Radon-Nikodym 导数”奈良教育大学公告 40. 1-7 (1991)。
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相似海外基金
部分環の指数とエントロピ-に関する研究
子环指数与熵的研究
- 批准号:
02640123 - 财政年份:1990
- 资助金额:
$ 1.09万 - 项目类别:
Grant-in-Aid for General Scientific Research (C)