Cyclicity of coefficient multipliers: Linear structure |
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Authors: | L Bernal-gonzález M C Calderón-Moreno J A Prado-Bassas |
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Institution: | (1) Departamento de Análisis Matemático, Universidad de Sevilla, Apdo. 1160, Avda. Reina Mercedes, 41080 Sevilla, Spain |
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Abstract: | We characterize various kinds of cyclicity of sequences of coefficient multipliers, which are operators defined on spaces
of holomorphic functions. In the case of a single coefficient multiplier we characterize its cyclicity, which contrasts with
the fact that such operators are never supercyclic. Moreover, it is proved that for each cyclic function there is a dense
part of the linear span of its orbit all of whose vectors are cyclic.
The authors have been partially supported by MCYT Grants BFM2003-03893-C02-01, MTM2004-21420-E and Plan Andaluz de Investigación
Junta de Andalucía FQM-127. |
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Keywords: | cyclicity supercyclicity hypercyclicity coefficient multiplier Euler differential operator Hadamard operator |
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