不变子空间和约化子空间问题是泛函分析中的一个基本问题。算子的交换子和相似度可以帮助理解算子的结构。Toplitz算子是算子理论中一类重要的算子。算子的相似性是泛函分析中与不变子空间和约化子空间问题相关的一个有趣的话题。该书总结了Bergman空间、Dirichlet空间等解析函数空间中的相似和约化子空间问题。研究方法包括算子理论与无穷矩阵操作相结合的技术。本书主要面向泛函分析算子理论方向研究生以及相关方向的科研人员。
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199009-199406 河北师范大学本科
199609-199906 河北师范大学硕士
200409-200706 河北师范大学博士
201507-201601 The University of Toledo 高级访问学者199407-至今 河北师范大学基础数学 算子理论与算子代数在Journal of Mathematical Analysis and Applications、Integral Equations and Operator Theory、Science in China (Series A)、Acta Mathematica Sinica (English Series)等刊物发表论文20多篇；参编《复变函数》（高等教育出版社）教材一部
Contents
Preface i
CHAPTER 1
Operator on the Bergman Space 1
1.1 Similarity Invariant of Analytic Toeplitz Operators 1
1.2 Commutant of Analytic Toeplitz Operators 17
1.3 Compactness of a Class of Radial Operators 31
1.4 Similarity of a Class of Multiplication Operators 42
1.5 r^Berezin Transform and Radial Operator 57
1.6 A Class of Hilbert-Schmidt Operators on the Harmonic Bergman Space 71
1.7 The Operator Mznzn on Subspaces of Bergman Spaces over the Biannulus 83
1.8 Local Quasi-Similarity and Reducing Subspaces of Multiplication Operator 97
1.9 Quasi-Affinity and Reducing Subspaces of Multiplication Operator 106
1.10 Remarks 115
CHAPTER 2
Operator on the Dirichlet Space 117
2.1 Similarity and Commutant of a Class of Multiplication Operators 117
2.2 The Properties of Canonical Solution Operator to d 131
2.3 Compactness of Hankel Operators 141
2.4 Remarks 158
CHAPTER 3
Operator on the Fock Space 161
Quasi-Similarity and Reducing Subspaces of Multiplication Operator 161
The Norm of Hankel Operator Restricted to the Fock Space 168
Remarks 176
CHAPTER 4
Operator on the Soblev Disk Algebra 179
4.1 Similarity and Reducing Subspaces of Multiplication Operator 179
4.2 Remarks 185
CHAPTER 5
Operator on Banach Algebra 187
5.1 Algebra Matrix and Similarity Classification of Operators 187
5.2 Remarks 197
Conclusion 199
References 201
List of Symbols and Notations 207
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