FUNCTIONAL CALCULI FOR SECTORIAL OPERATORS AND RELATED FUNCTION THEORY
We construct two bounded functional calculi for sectorial operators on Banach spaces, which enhance the functional calculus for analytic Besov functions, by extending the class of functions, generalising and sharpening estimates and adapting the calculus to the angle of sectoriality. The calculi are...
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| Veröffentlicht in: | Journal of the Institute of Mathematics of Jussieu 2023-05, Vol.22 (3), p.1383-1463 |
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| container_title | Journal of the Institute of Mathematics of Jussieu |
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| creator | Batty, Charles Gomilko, Alexander Tomilov, Yuri |
| description | We construct two bounded functional calculi for sectorial operators on Banach spaces, which enhance the functional calculus for analytic Besov functions, by extending the class of functions, generalising and sharpening estimates and adapting the calculus to the angle of sectoriality. The calculi are based on appropriate reproducing formulas, they are compatible with standard functional calculi and they admit appropriate convergence lemmas and spectral mapping theorems. To achieve this, we develop the theory of associated function spaces in ways that are interesting and significant. As consequences of our calculi, we derive several well-known operator norm estimates and provide generalisations of some of them. |
| doi_str_mv | 10.1017/S1474748021000414 |
| format | Article |
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The calculi are based on appropriate reproducing formulas, they are compatible with standard functional calculi and they admit appropriate convergence lemmas and spectral mapping theorems. To achieve this, we develop the theory of associated function spaces in ways that are interesting and significant. As consequences of our calculi, we derive several well-known operator norm estimates and provide generalisations of some of them.</description><identifier>ISSN: 1474-7480</identifier><identifier>EISSN: 1475-3030</identifier><identifier>DOI: 10.1017/S1474748021000414</identifier><language>eng</language><publisher>Cambridge, UK: Cambridge University Press</publisher><subject>Algebra ; Banach spaces ; Calculi ; Calculus ; Estimates ; Function space ; Functionals ; Generators ; Hilbert space ; Mathematical analysis ; Operators (mathematics)</subject><ispartof>Journal of the Institute of Mathematics of Jussieu, 2023-05, Vol.22 (3), p.1383-1463</ispartof><rights>The Author(s), 2021. 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Inst. Math. Jussieu</addtitle><description>We construct two bounded functional calculi for sectorial operators on Banach spaces, which enhance the functional calculus for analytic Besov functions, by extending the class of functions, generalising and sharpening estimates and adapting the calculus to the angle of sectoriality. The calculi are based on appropriate reproducing formulas, they are compatible with standard functional calculi and they admit appropriate convergence lemmas and spectral mapping theorems. To achieve this, we develop the theory of associated function spaces in ways that are interesting and significant. 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| language | eng |
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| source | Cambridge University Press Journals Complete |
| subjects | Algebra Banach spaces Calculi Calculus Estimates Function space Functionals Generators Hilbert space Mathematical analysis Operators (mathematics) |
| title | FUNCTIONAL CALCULI FOR SECTORIAL OPERATORS AND RELATED FUNCTION THEORY |
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