Application of entropy theory to the problem of data compression

（一）;在可分离的希尔伯特空间上用一些核操作员家族构建了新的本地卷积拓扑，其中的拓扑结构比正常拓扑结构更弱，比较弱的拓扑结构更强。这些主题被应用于核操作员的分类。进一步，核操作员下封闭单元球范围内的子空间的同源性问题被处理了。This result is applied to the homeomorphism problem of periodic and continuously differentiable function spaces included by LイイD12イエD1[0，1]。（二）; Homomorphism问题的子空间和规范在术语范围内的封闭单元球在紧凑型积极运算符下被检查。这些结果将被应用到复制内核希尔伯特空间的操作员理论分类中。（三）; It is shown that Ohya's entropy dimension on a W-D1 *-dynamical system is time-invariant， and homeomorphism problems of operator algebras equipped with the quasi σ-strong operator topies are discussed。（四）;一个公式，用于估计ε-在一个紧凑型阳性运算符中，这种运算符的实际价值分布的术语是由Prosser和Root提供的。在本文中，一个用于估计在一个紧凑型阳性运算符中分配的正确价值的数值的转换公式是给定的。（五）;在局部卷积拓扑向量空间上的紧凑非线性映射的同源性问题已研究在维度理论的方法下。第一个是所有的，维度理论同源性变量，定义了所有紧凑型非线性映射集的变体。然后，这些变量被应用到固定点的维度理论特征中，这些紧凑型非线性映射已经存在。

(1). New locally convex topologies constructed with some families of nuclear operators on a separable Hilbert space which are weaker than the norm topology and stronger than the weak topology are given. These topologies are applied to the classification of nuclear operators. Further, the homeomorphism problem of subspaces with the norms in terms of the ranges of the closed unit ball under nuclear operators is treated. This result is applied to the homeomorphism problem of periodic and continuously differentiable function spaces included by LィイD12ィエD1[0,1].(2). The homeomorphism problems of subspaces with norms in terms of the ranges of the closed unit ball under compact positive operators are examined. These results will be applied to the operator theoretical classification of reproducing kernel Hilbert spaces.(3). It is shown that Ohya's entropy dimension on a WィイD1*ィエD1-dynamical system is time-invariant, and homeomorphism problems of operator algebras equipped with the quasi σ-strong operator topologies are discussed.(4). A formula for estimating ε-entropy of a compact positive operator in terms of the distribution of proper values of such an operator was given by Prosser and Root. In this paper, an inversion formula for estimating the distribution of proper values of a compact positive operator in terms of ε-entropy of such an operator is given.(5). The homeomorphism problem of compact nonlinear mappings on a locally convex topological vector space is studied under the method of dimension theory. First of all, dimension theoretic homeomorphism invariants which are defined on the set of all compact nonlinear mappings are introduced. Next, these invariants are applied to dimension theoretic characterization of the fixed point sets which these compact nonlinear mapping have.