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Related topics on Operator Theory and Operator Algebras

有关算子理论和算子代数的相关主题

基本信息

批准号：
15540198
负责人：
NAGISA Masaru
金额：
$ 1.98万
依托单位：
Chiba University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2003
资助国家：
日本
起止时间：
2003 至 2005
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15540198/
关键词：
completely positive map completely bounded map operator space numerical radius Schur multiplier Haagerup tensor product numerical radius operator space operator algebra シュア-積モジュール写像可換子表現写像の分解

项目摘要

Our interest of this research is in the intersection area of Operator Theory and Operator Algebra.One of main results is to characterize the numerical radius norm of Schur multipiers. U.Haagerup refound the characterization of the norm of Schur multiplier and he constructed the theory of Haagerup tensor product of operator spaces. T.Ando proved the similar characterization of the numerical radius norm of Schur multipliers for matrices. Our result is extended vesion of Ando's result.Next result is concerned with operator spaces. As an application of abobe result, we consider linear spaces with matrix norms. Usual norms implies the structure of operator spaces. We consider numerical radius norms instead of usual norms. We call it numerical radius operator space. Z.-J.Ruan proved that every operator spaces can be realized as a subspace of B(H) with usual norms, where B(H) is the set of all bounded linear operators on a Hilbert space H. We can show the similar result for numerical radius operator spaces, that is, every numerical radius operator spaces can be realized as a subspace of B(H) with numerical radius norms. This result contains Ruans' result as a special case.

本文的研究工作是在算子理论与算子代数的交叉领域进行的，主要结果之一是刻画了Schur多重支墩的数值半径范数。Haagerup重新发现了Schur乘子范数的特征，并建立了算子空间的Haagerup张量积理论。T.Ando证明了矩阵Schur乘子的数值半径范数的相似刻画。我们的结果是Ando结果的推广，下一个结果是关于算子空间的。作为abobe结果的一个应用，我们考虑了具有矩阵范数的线性空间。代数范数蕴含了算子空间的结构。我们考虑数值半径范数而不是通常的范数。我们称之为数值半径算子空间。Z.- J.Ruan证明了每一个算子空间都可以实现为B（H）的具有通常范数的子空间，其中B（H）是Hilbert空间H上所有有界线性算子的集合。对于数值半径算子空间，我们也得到了类似的结果，即每个数值半径算子空间都可以实现为B（H）的具有数值半径范数的子空间.这个结果包含了Ruans的结果作为一个特例.