Chapter 1. Introduction 1.1. Existence of hypercyclic algebras 1.2. Common hypercyclic algebras 1.3. Frequently and upper frequently hypercyclic algebras 1.4. Disjoint hypercyclic algebras 1.5. Organization of the paper 1.6. Notations Chapter 2. A general criterion 2.1. A transitivity criterion to get hypercyclic algebras 2.2. Hypercyclic algebras not contained in a finitely generated algebra Chapter 3. Convolution operators with |φ(0)| > 1 3.1. Operators with many eigenvectors 3.2. Applications to convolution operators Chapter 4. Weighted shifts on Fréchet sequence algebras 4.1. Fréchet sequence algebras with the coordinatewise product 4.2. Bilateral shifts on Fréchet sequence algebras with the coordinatewise product 4.3. Fréchet sequence algebras for the convolution product Chapter 5. Common hypercyclic algebras 5.1. How to get a common hypercyclic algebra 5.2. Common hypercyclic algebras for a family of backward shiftscoordinatewise product 5.3. Common hypercyclic algebras for a family of backward shifts -Cauchy product Chapter 6. Frequently and upper frequently hypercyclic algebras 6.1. How to get upper frequently hypercyclic algebras 6.2. Existence of upper frequently hypercyclic algebras for weighted backward shifts -coordinatewise products 6.3. Existence of upper frequently hypercyclic algebras for weighted backward shifts -convolution product 6.4. Weighted shifts with a frequently hypercyclic algebra on ω 6.5. A sequence of sets with positive lower density which are very far away from each other 6.6. A weighted shift with a frequently hypercyclic algebra on c 0 Chapter 7. Disjoint hypercyclic algebras iii iv CONTENTS 7.1. How to get a disjoint hypercyclic algebra 7.2. Disjoint hypercyclic algebras for backward shifts -coordinatewise product 7.3. Disjoint hypercyclic algebras for backward shifts -convolution product Chapter 8. Concluding remarks and open questions 8.1. Closed hypercyclic algebras 8.2. Hypercyclic algebras in the ideal of compact operators 8.3. Further question and remark Bibliography
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