Article
Strongly omnipresent operators: general conditions and applications to composition operators
Author/s | Bernal González, Luis
Calderón Moreno, María del Carmen Grosse-Erdmann, Karl-Goswin |
Department | Universidad de Sevilla. Departamento de Análisis Matemático |
Publication Date | 2002-06 |
Deposit Date | 2019-06-18 |
Published in |
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Abstract | This paper studies the concept of strongly omnipresent operators that was recently introduced by the first two authors. An operator T on the space H(G) of holomorphic functions on a complex domain G is called strongly ... This paper studies the concept of strongly omnipresent operators that was recently introduced by the first two authors. An operator T on the space H(G) of holomorphic functions on a complex domain G is called strongly omnipresent whenever the set of T-monsters is residual in H(G), and a T-monster is a function f such that T f exhibits an extremely ‘wild’ behaviour near the boundary. We obtain sufficient conditions under which an operator is strongly omnipresent, in particular, we show that every onto linear operator is strongly omnipresent. Using these criteria we completely characterize strongly omnipresent composition and multiplication operators. |
Project ID. | PB96-1348 |
Citation | Bernal González, L., Calderón Moreno, M.d.C. y Grosse-Erdmann, K. (2002). Strongly omnipresent operators: general conditions and applications to composition operators. Journal of the Australian Mathematical Society, 72 (3), 335-348. |
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