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1·Naught space properties of compact linear operator in normed space;

证明了模糊赋范空间上有界线性算子的一个保范延拓定理。

2·For doubling measure, the boundedness of the sub-linear operator plays an important role in many problems.

在双倍测度下，次线性算子有界性问题的研究起到非常重要的作用。

3·And this definition is very important for us to study the topological inner inverse for a linear operator in a topological Spaces.

该定义对研究拓扑空间中线性算子的拓扑内逆具有重要意义。

4·By using linear operator theory in L2 space, we get the distributed parameters on real line and the existence of positive solutions.

藉助L_2空间上的线性算子理论，我们得到了这类方程的控制参数在实轴上的分布情况以及存在符合物理意义的正解的条件。

5·By using linear operator theory in L2 space, we proved that the operators of this kind has not more than denumerable positive eigenvalues.

运用L2空间上的线性算子理论，我们证明了这类算子存在至多可数个正的本征值。

6·We build a set of complete bases through resolving the eigenvalue problem of this linear operator and prove its completeness and orthogonality.

通过解这一线性算符的本征值问题，构造一组完备基，并给出完备性和正交性的证明；

7·By using the semigroup of bounded linear operator, a new locally convex vector topological is introduced, and some propositions of it are given.

利用有界线性算子半群，引入了一新的局部凸向量拓扑，并对其基本性质进行了讨论。

8·By using the C-semigroup of bounded linear operator, a new locally convex vector topological is introduced, and some propositions of it are given.

利用C -半群的概念，引入一新的局部凸向量拓扑，并对其基本性质以及在新的局部凸线性拓扑意义下c -半群的性质进行初步研究。

9·Then T is an invertible linear operator preserving rank - partial ordering on Sn(F) if and only if there exists an invertible matrix (F) such that where .

刻画了在非负无零因子交换半环上强保持可逆矩阵的线性算子。

10·Since the coefficient of the new polynomial is too complicate to calculate directly, we introduce a linear operator and study the algebraic properties of it.

该多项式的系数较为复杂，难以直接计算。 我们引进了一个线性算子并研究了其性质。