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Ringrose began to study nest algebras in the 1960s, many people have devoted themselves to the study of non-selfadjoint and reflexive operator algebras including nest algebras, commutative subspace lattice algebras, completely distributive subspace lattice algebras and so on, and obtain a lot of beautiful achievements.

自从60年代J.Ringrose开始研究套代数以来,人们对套代数、交换子空间格代数和完全分配子空间格代数等非自伴自反算子代数进行了深入研究,并且取得了大量出色的研究成果。

About Dirac eigenvalue problem with general two points' liner algebra, corresponding operator of which often is non-self-adjoint operator.

对于一般两点线性边界条件下的Dirac特征值问题,相应的算子一般说是非自伴的

Firstly,by using the estimating methodfor the compact embedding operators(from weighted Sobolev space to the weighted〓space),we obtain a necessary and sufficient condition for the discreteness of thespectrum of certain differential operators.Secondly,based on the property of thespectrum of difinitizable operators on the Krein space,we consider the left definitedifferential equations with middle deficiency indices,and give a completecharacterization for self-adjoint(J-self-adjoint)differential operators in theindefinite inner product space 〓.Especially,we prove that all the J-self-adjoint differential operators are definitizable.

我们首先运用加权Sobolev空间到加权〓空间嵌入算子紧性的判别方法,证明一类加权自伴微分算子具有离散谱的充要条件;然后,基于Krein空间上可定化算子谱的性质,对于具中间亏指数的左定型微分方程,建立其相应的微分算式在不定度规空间〓上所生成自伴算子的完备性刻画(特别证明了J-自伴微分算子具有可定化性)。

In chapter three, I study the isometric maps on non-self-adjoit AF C* algebra..

第三章中,主要是对非自伴的AF C~*-代数,讨论了它上面的等距映射。

The class of non-selfadjoint operator algebras is an important domain in operator algebras reaserching.

非自伴算子代数是算子代数中一个重要的研究领域,而套代数是一类最重要的非自伴算子代数。

We also give all positive self-adjoint extensions ofsingular differential operators,and all positive self-adjoint operators generated by theproducts of differential expressions 〓,where l is an nth order differentialexpression.The result that each positive self-adjoint operator is not necessarily theform of operator product 〓.This answers an open problem proposed by theauthors recently.

我们也给出了奇型微分算子的所有正自伴扩张形式及乘积微分算式〓所诱导的所有正自伴算子形式,证明〓所诱出的正自伴算子不必须是由算子乘积〓为l所生成的算子)的形式,从而回答了作者新近提出的一个公开问题。

AF C*-algebra is the self-adjoint limit algebra, so it has relatively complex structure.

AF代数是自伴的极限代数,因而结构比较复杂。

We discuss a class of second order self-adjoint matrix differential systems with damping term and self-adjoint Hamiltonian matrix differential systems, etc.

在第五、六章中,考虑一类线性泛函g和一类对s偏导数不一定非正的Hk型函数,分别研究了自伴的带有阻尼项的二阶矩阵微分系统和自共轭的Hamilton矩阵微分系统。

In Chapter 3, we discuss the self-adjoint boundary-value problems for products of m differential operators generated by the same symmetric differential expression of order n defined on a, b

第三章 讨论了m个由同一n阶对称微分算式生成的赋予某种边界条件的微分算子乘积自伴边值问题,结合常微分算子自伴扩张的一般构造理论,分别给出了两个四阶微分算子、两个n阶微分算子、m个n阶微分算子乘积自伴边条件的解析刻划,得到了乘积微分算子是自伴的充分必要条件及与乘积算子自伴性有关的一些有益结果。

In Chapter 3,applying the results of the Chapter 1 and 2,we discusssystematically the bound restricting self-adjoint extensions for Sturm-Liouvilleoperator 〓,i.e.,for any constant〓,we find all the possible self-adjoint extensionsL,such that their minimal engenvalue is exactly equal to 〓.

第三章 应用前两章所发展的一般理论,更详尽地讨论Sturm-Liouville微分算子〓的限界自伴扩张(即刻画〓的所有可能自伴扩张L使L以预先给定的常数〓为最小特征值)。

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随着死亡的吉他手Schuldiner接受主唱的职务,乐队在现实中树立了重要的影响。

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