فضاهای تابع در تحلیل: کنفرانس هفتم، فضاهای تابع، ۲۰-۲۴ مه ۲۰۱۴: دانشگاه ایلی‌نوی جنوبی، ادواردزویل (ریاضیات معاصر)

This volume contains the proceedings of the Seventh Conference on Function Spaces, which was held from May 20–24, 2014 at Southern Illinois University at Edwardsville. The papers cover a broad range of topics, including spaces and algebras of analytic functions of one and of many variables (and operators on such spaces), spaces of integrable functions, spaces of Banach-valued functions, isometries of function spaces, geometry of Banach spaces, and other related subjects. Cover 1 Title page 4 Contents 6 Preface 8 On algebraic properties of the spectrum and spectral radius of elements in a unital algebra 10 1. Introduction 10 2. Results about elements in the center of an algebra 11 3. Results about the case when two elements of an algebra coincide 12 4. Application to the case of linear operators 14 5. Results on discs on complex plane which contain the spectrum of an element 16 References 21 Automatic continuity of surjective homomorphisms between topological algebras 22 1. Introduction 23 2. Main result 26 References 29 Characterization of Holomorphic and Meromorphic Functions via Maximum Principles 32 1. Modules over the disk algebra 32 2. Modules over the polydisk and ball algebras 34 References 36 Hermitian operators on H^{p}_{H}(\trianglen) 38 1. Introduction 38 2. One-parameter groups of isometries on H^{p}_{}H(\trianglen) 39 3. The Generator of one-parameter groups of isometries on H^{p}_{}H(\trianglen) 45 4. Hermitian Operators on H^{p}_{}H(\triangle) 46 5. Hermitian operators on H^{p}_{}H(\trianglen): The pure elliptic case 53 References 55 Some notions of transitivity for operator spaces 58 1. Introduction 58 2. Absolute matrix convex transitivity 61 3. Matrix-level transitivity: proof of Theorem 1.5 66 4. Theorem 1.8: the construction 67 References 69 Removability of exceptional sets for differentiable and Lipschitz functions 72 1. Introduction 72 2. Pointwise Lipschitz constants 73 References 76 Generalizing trigonometric functions from different points of view 78 1. Analytic point of view 79 2. Geometric point of view 81 3. An integral operator and generalized trigonometric functions 82 4. Eigenfunctions for the p-Laplacian 83 5. The approximation theory point of view and the generalization of trigonometric functions 84 6. Some other definitions of generalized trigonometric functions 87 References 89 Partial W*-dynamical systems and their dilations 92 1. Introduction 92 2. Basic structures and notions 93 3. Competely positive maps 97 4. Partial W*-dynamical systems 97 5. *-Biautomorphisms 98 6. Dilations of partial W*-dynamical systems 99 7. Generators and *-biderivations 100 Acknowledgement 104 References 105 Swiss Cheeses and Their Applications 108 1. Introduction 108 2. Preliminaries 109 3. Swiss cheeses 111 4. Examples of Swiss cheese sets 113 5. Classicalisation theorems 116 6. Comparison of Swiss cheeses 117 7. Semiclassicalisation 119 8. A classical counterexample to the conjecture of S. E. Morris 123 9. Open questions 125 References 126 Isometries on the special unitary group 128 1. Introduction and statement of the main result 128 2. Preparation of the proof that (i) implies (ii) 129 3. Completion of the proof of Theorem 1.1 141 Acknowledgements 142 References 142 Amenability as a hereditary property in some algebras of vector-valued functions 144 1. Introduction 144 2. Amenability in section spaces of bundles of Banach algebras 146 References 152 Weighted norm inequalities for Hardy type operators on monotone functions 154 1. Introduction 154 2. Historical Remarks and Present Agenda 155 3. The operator Sφ on non-increasing functions 157 4. The operator S*φ on non-increasing functions 161 5. The operator Sφ on non-decreasing functions 164 References 167 Norms on normal function algebras 170 References 172 Maximally Modulated Singular Integral Operators and their Applications to Pseudodifferential Operators on Banach Function Spaces 174 1. Introduction 174 2. Preliminaries 177 3. Maximally modulated singular integrals on Banach function spaces 180 4. Boundedness of pseudodifferential operators with non-regular symbols on Banach function spaces 181 5. Boundedness of maximally modulated Calderón-Zygmund operators and pseudodifferential operators with non-regular symbols on variable Lebesgue spaces 183 6. Compactness of pseudodifferential operators with non-regular symbols on variable Lebesgue spaces 184 References 186 Smoothness to the Boundary of Biholomorphic Mappings: An Overview 188 1. Introduction 188 2. Discussion of Fefferman’s Techniques 191 3. New Directions of Webster, Bergman, Bell, and Bell/Ligocka 193 4. Refined Results 195 5. More Recent Results 196 6. Proper Holomorphic Mappings 196 7. Concluding Remarks 197 References 197 A multiplicative Banach-Stone theorem 200 1. Introduction 200 2. Notation and Preliminary Results 202 3. Proof of Main Theorem 203 References 205 Weighted composition operators on weighted sequence spaces 208 1. Introduction 208 2. Invariance and boundedness 209 3. Compactness and compact difference 212 4. Essential norm 216 5. Closed range 219 6. Multiplication and composition operators 223 Acknowledgment 224 References 224 Spectral isometries into commutative Banach algebras 226 1. Introduction 226 2. Non-unital and non-surjective spectral isometries 227 References 231 Eigenvalues and eigenfunctions of the p(⋅)-Laplacian. A convergence analysis 232 1. Spaces and embeddings 232 2. Spectral theory of the p(⋅)-Laplacian 233 3. Concluding remarks 237 References 237 Surjective isometries between function spaces 240 1. Introduction 240 2. Main results 240 Acknowledgement 247 References 248 Endomorphisms and the Šilov Representation 250 1. Introduction 250 2. Definitions, Notation and Standard constructions 251 3. Endomorphisms of Šilov Algebras 253 4. Closing Remarks 256 References 256 The essential norm of operators on the Bergman space of vector–valued functions on the unit ball 258 1. Introduction and Statement of Main Results 258 2. Preliminaries 260 3. Approximation By Localized Compact Operators 269 4. A Uniform Algebra and its Maximal ideal Space 275 5. Characterization of the Essential Norm on Weighted Bergman Spaces 282 6. Acknowledgements 289 References 289 Trigonometric approximation of periodic functions belonging to weighted Lipschitz class W(L^{p},Ψ(t),β) 292 1. Introduction 292 2. Main Results 294 3. Lemmas 295 4. Proof of Theorem 2.1 295 5. Proof of Theorem 2.3 297 6. Corollaries 298 References 299 Analytic structure of polynomial hulls 302 1. Introduction 302 2. Browder’s Theorem 304 3. Examples 304 4. Work of Gromov and Alexander 307 References 309 Back Cover 314