SCHWARZ NORMS IN OPERATOR ALGEBRAS AND CONTRACTIONS, AND ITS APPLICATIONS TO DIFFERENTIAL OPERATORS

算子代数和收缩中的施瓦茨范数及其在微分算子中的应用

基本信息

批准号：
09640200
负责人：
UCHIYAMA Mitsuru
金额：
$ 1.54万
依托单位：
FUKUOKA UNIVERSITY OF EDUCATION
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 1998
项目状态：
已结题

项目摘要

The research results which we have gotten with a support of GRANT TN AID for SEIENTIFIC RESEARCH (C) are 5 published papers, 3 accepted papers and I submitted paper. The content of them are as follows :1. For non-negative operators (or matrices) A, B, and for an operator nonotone function f, we hadllf (A) f (B) ll * f (ROO<>llABll)^2Especially, for the norms of products of logarithmic funtions we hadlllog (1 A) log (1+ B) ll * log (1+ ROO<>llABll)^2Moreover these are extended to the case of real number powers, so it may be called Minkowski-type inequality. Furthur we investigated and showed that similar Minkowski-type inequality holds for determinants.Mathematical Inequality and Appl.Vol.1(2)(1998)279-284.2. Furuta extended the Heinz-Kato Inequality. We extended it as follows :For operator monotone functions f(t), g(t) >0, T(fg/t)(ITI) is well defined for every T and satisfies T(fg/t)(ITI)x, y ) * (f(ITI)x, x)(g(ITI )y.y) for all vectors x, yProc. Amer.Math. Soc.3. We studied Korovkin theory in C^*-algebras. We found a new inequality whch is very useful to study Korovkin theory. By making use of it, we made clear the the proofs of known theorems and got new Korovkin sets.Mathinatishe Zeitshrift4. The function f is called an operator monotone function if for operators A, B0* f(A) * f(B) whenever 0* A * BWe showed that if f is an operator monotone function and if f is not rational, then f is strongly monotone.

我们在支持SEINIDIFIC研究援助的支持下获得的研究结果是5篇已发表的论文，3篇接受的论文，我提交了论文。它们的内容如下：1。对于非负操作员（或矩阵）a，b，对于操作员非旋翼函数f，我们hadllf（a）f（b）ll * f（roo <> llabll）^2尤其是对数函数产物的规范，我们hedllog（1 a）log（1 a）log（1+ b）ll * log y ro.数字功能，因此可以称为Minkowski型不等式。除此之外，我们调查并表明类似的Minkowski型不等式适用于决定因素。数学不平等和Appl.Vol.1（2）（1998）279-284.2。 Furuta扩大了Heinz-Kato的不平等。我们将其扩展如下：对于操作员单调函数f（t），g（t）> 0，t（fg/t）（iti）对每个t的定义很好，并且满足t（fg/t）（iti）x，y） *（f（iti）x，x，x，x）（g（iti）y.y）（g（iti）y.y），用于所有vectors x，yproc。 Amer.math。 Soc.3。我们研究了C^* - 代数的Korovkin理论。我们发现一种新的不平等对研究科罗夫金理论非常有用。通过使用它，我们清楚地清楚了已知定理的证据，并获得了新的Korovkin set.Mathinatishe Zeitshrift4。如果对于操作员A，B0 * f（a） * f（b），则函数f被称为单调函数。