EDP Sciences 1775654260 20260408 fre

laboutique.edpsciences.fr-R002706 03 01 01 R002706 00 ED E107 00 01 01 Similarity of Operator on Analytic Function Spaces 01 eng 08 218 03 22 2341158 17 01 P15 EDP Sciences & Science Press 01 01 P15 EDP Sciences & Science Press 11 00 20250424 02 01 002885 03 9782759837298 15 9782759837298 03 01 D1 EDP Sciences 45 03 laboutique.edpsciences.fr-002885 03 01 01 002885 03 9782759837298 15 9782759837298 10 EA E107 10 00 01 R002706 ED E107 1 10 01 02 Current Natural Sciences 01 01 Similarity of Operator on Analytic Function Spaces 1 A01 01 A2342 Yucheng Li Li, Yucheng Yucheng Li Yucheng Li is a professor at Hebei Normal University, whose main research interests are function spaces and operator theory. 01 eng 08 216 03 01 20 Similarity;multiplication operators;Bergman space;Dirichlet space;Sobolev disc algebra;Hankel operators;weighted Bergman space;operator theory techniques;infinite matrix manipulations;commutant;Toeplitz operators;finite Blaschke product;monomial symbol;Fock space;algebra matrix;Cowen-Douglas operators;single-variable complex analysis;operator theory. 10 2011 MAT037000 29 CLIL3052 01 510 05 03 00 This book summarizes the study of similarity and reducing subspaces for a class of multiplication operators on the Bergman space, Dirichlet space, and Sobolev disc algebra.It also investigates the compactness of certain radial and Hankel operators on the weighted Bergman space. The research methods combine operator theory techniques with infinite matrix manipulations.The book consists of five chapters. In the first chapter, we characterize the similarity and commutant of certain analytic Toeplitz operators. The second chapter focuses on the similarity of multiplication operator induced by finite Blaschke product and characterize the compactness of a class of Hankel operators. The third chapter discusses the quasi-similarity and reducing subspaces of a class of multiplication operator with monomial symbol in the Fock space. The fourth chapter explores the similarity and reducing subspaces of a class of multiplication operator induced by monomial symbol in the Sobolev disc algebra. The fifth chapter addresses the algebra matrix and similarity classification of certain Cowen-Douglas operators.The theme of the book is straightforward. Its contents can be comfortably understood by readers with a background in single-variable complex analysis and basic knowledge of operator theory. 02 00 This book summarizes the study of similarity and reducing subspaces for a class of multiplication operators on the Bergman space, Dirichlet space, and Sobolev disc algebra.It also investigates the compactness of certain radial and Hankel operators on the weighted Bergman space. The research methods combine operator theory techniques with infinite matrix manipulations. 04 00 Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IIICHAPTER 1Operator on the Bergman Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Similarity Invariant of Analytic Toeplitz Operators . . . . . . . . . . . . . . . 11.2 Commutant of Analytic Toeplitz Operators. . . . . . . . . . . . . . . . . . . . . 171.3 Compactness of a Class of Radial Operators . . . . . . . . . . . . . . . . . . . . 311.4 Similarity of a Class of Multiplication Operators . . . . . . . . . . . . . . . . . 421.5 n-Berezin Transform and Radial Operator . . . . . . . . . . . . . . . . . . . . . . 571.6 A Class of Hilbert–Schmidt Operators on the Harmonic Bergman Space . . .. . . .. 711.7 The Operator Mzn1zn2 on Subspaces of Bergman Spaces over the Biannulus .. . . . . . . . . 831.8 Local Quasi-Similarity and Reducing Subspaces of Multiplication Operator . . ... . . . . . 971.9 Quasi-Affinity and Reducing Subspaces of Multiplication Operator . . . 1061.10 Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115CHAPTER 2Operator on the Dirichlet Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1172.1 Similarity and Commutant of a Class of Multiplication Operators . . . . 1172.2 The Properties of Canonical Solution Operator to @ . . . . . . . . . . . . . . 1312.3 Compactness of Hankel Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1442.4 Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158CHAPTER 3Operator on the Fock Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1613.1 Quasi-Similarity and Reducing Subspaces of Multiplication Operator . 1613.2 The Norm of Hankel Operator Restricted to the Fock Space . . . . . . . . 1683.3 Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176CHAPTER 4Operator on the Sobolev Disk Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1794.1 Similarity and Reducing Subspaces of Multiplication Operator . . . . . . 1794.2 Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185CHAPTER 5Operator on Banach Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1875.1 Algebra Matrix and Similarity Classification of Operators . . . . . . . . . . 1875.2 Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201List of Symbols and Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 21 00 06 01 https://laboutique.edpsciences.fr/produit/1478/9782759837298/similarity-of-operator-on-analytic-function-spaces 01 00 03 02 https://laboutique.edpsciences.fr/system/product_pictures/data/009/983/357/original/9782759837281-Similarity_of_Operator_on_Analytic_Function_Spaces_couv-sofedis.jpg 17 14 20250319T182711+0100 01 P15 EDP Sciences & Science Press 01 01 P15 EDP Sciences & Science Press 04 11 00 20250424 01 00 20250424 19 00 20250424 2026 06 3052868830012 01 WORLD 13 03 9782759837281 15 9782759837281 WORLD 08 EDP Sciences & Science Press 04 01 00 20250424 03 01 D1 EDP Sciences 20 04 05 01 02 1 00 52.99 01 5.50 2.76 EUR 04 06 01 02 1 00 187.99 01 5.50 2.76 EUR 01 04 06 01 02 1 00 206.99 01 5.50 10.79 USD 01