Essential norm of Cesàro operators on L and Cesàro spaces
| Autor: | Georges Habib, Ihab Al Alam, Fares Maalouf, Loïc Gaillard, Pascal Lefèvre |
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| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
Mathematics::Dynamical Systems Measurable function Applied Mathematics 010102 general mathematics Banach space Compact operator 01 natural sciences 010101 applied mathematics Operator (computer programming) Multiplication operator Norm (mathematics) 0101 mathematics Analysis Mathematics |
| Zdroj: | Journal of Mathematical Analysis and Applications. 467:1038-1065 |
| ISSN: | 0022-247X |
| DOI: | 10.1016/j.jmaa.2018.07.038 |
| Popis: | In this paper, we consider the Cesaro-mean operator Γ acting on some Banach spaces of measurable functions on ( 0 , 1 ) , as well as its discrete version on some sequences spaces. We compute the essential norm of this operator on L p ( [ 0 , 1 ] ) , for p ∈ ( 1 , + ∞ ] and show that its value is the same as its norm: p / ( p − 1 ) . The result also holds in the discrete case. On Cesaro spaces the essential norm of Γ turns out to be 1. At last, we introduce the Muntz–Cesaro spaces and study some of their geometrical properties. In this framework, we also compute the value of the essential norm of the Cesaro operator and the multiplication operator restricted to those Muntz–Cesaro spaces. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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