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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