A Katznelson-Tzafriri theorem for analytic Besov functions of operators
Let T be a power-bounded operator on a Banach space X, A be a Banach algebra of bounded holomorphic functions on the unit disc D, and assume that there is a bounded functional calculus for the operator T, so there is a bounded algebra homomorphism mapping functions f ∈ A to bounded operators f(T) on...
| Auteurs principaux: | , |
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| Format: | Journal article |
| Langue: | English |
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Theta Foundation
2024
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| _version_ | 1826313924307320832 |
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| author | Batty, C Seifert, D |
| author_facet | Batty, C Seifert, D |
| author_sort | Batty, C |
| collection | OXFORD |
| description | Let T be a power-bounded operator on a Banach space X, A be a Banach algebra of bounded holomorphic functions on the unit disc D, and assume that there is a bounded functional calculus for the operator T, so there is a bounded algebra homomorphism mapping functions f ∈ A to bounded operators f(T) on X. Theorems of Katznelson-Tzafriri type establish that limn→∞ kT n f(T)k = 0 for functions f ∈ A whose boundary functions vanish on the unitary spectrum σ(T) ∩ T of T, or sometimes satisfy a stronger assumption of spectral synthesis. We consider the case when A is the Banach algebra B(D) of analytic Besov functions on D. We prove a Katznelson-Tzafriri theorem for the B(D)-calculus which extends several previous results. |
| first_indexed | 2024-03-07T07:21:44Z |
| format | Journal article |
| id | oxford-uuid:b7f733ff-6ab9-49f3-9ff4-a20f18d6e87f |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-09-25T04:24:03Z |
| publishDate | 2024 |
| publisher | Theta Foundation |
| record_format | dspace |
| spelling | oxford-uuid:b7f733ff-6ab9-49f3-9ff4-a20f18d6e87f2024-08-22T10:24:49ZA Katznelson-Tzafriri theorem for analytic Besov functions of operatorsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:b7f733ff-6ab9-49f3-9ff4-a20f18d6e87fEnglishSymplectic ElementsTheta Foundation2024Batty, CSeifert, DLet T be a power-bounded operator on a Banach space X, A be a Banach algebra of bounded holomorphic functions on the unit disc D, and assume that there is a bounded functional calculus for the operator T, so there is a bounded algebra homomorphism mapping functions f ∈ A to bounded operators f(T) on X. Theorems of Katznelson-Tzafriri type establish that limn→∞ kT n f(T)k = 0 for functions f ∈ A whose boundary functions vanish on the unitary spectrum σ(T) ∩ T of T, or sometimes satisfy a stronger assumption of spectral synthesis. We consider the case when A is the Banach algebra B(D) of analytic Besov functions on D. We prove a Katznelson-Tzafriri theorem for the B(D)-calculus which extends several previous results. |
| spellingShingle | Batty, C Seifert, D A Katznelson-Tzafriri theorem for analytic Besov functions of operators |
| title | A Katznelson-Tzafriri theorem for analytic Besov functions of operators |
| title_full | A Katznelson-Tzafriri theorem for analytic Besov functions of operators |
| title_fullStr | A Katznelson-Tzafriri theorem for analytic Besov functions of operators |
| title_full_unstemmed | A Katznelson-Tzafriri theorem for analytic Besov functions of operators |
| title_short | A Katznelson-Tzafriri theorem for analytic Besov functions of operators |
| title_sort | katznelson tzafriri theorem for analytic besov functions of operators |
| work_keys_str_mv | AT battyc akatznelsontzafriritheoremforanalyticbesovfunctionsofoperators AT seifertd akatznelsontzafriritheoremforanalyticbesovfunctionsofoperators AT battyc katznelsontzafriritheoremforanalyticbesovfunctionsofoperators AT seifertd katznelsontzafriritheoremforanalyticbesovfunctionsofoperators |