Algebrability of the set of everywhere surjective functions on C

We show that the set L of complex-valued everywhere surjective functions on C is aJgebrable. Specifically, L contains an infinitely generated algebra every non-zero element of which is everywhere surjective. We also give a technique to construct, for every n is an element of N, n algebraically indep...

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Detalles Bibliográficos
Autores: Aron, Richard M., Seoane Sepúlveda, Juan Benigno
Tipo de recurso: artículo
Fecha de publicación:2007
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/50466
Acceso en línea:https://hdl.handle.net/20.500.14352/50466
Access Level:acceso abierto
Palabra clave:517.98
Lineability
Spaceability
Algebrability
Everywhere surjective functions
Análisis funcional y teoría de operadores
Descripción
Sumario:We show that the set L of complex-valued everywhere surjective functions on C is aJgebrable. Specifically, L contains an infinitely generated algebra every non-zero element of which is everywhere surjective. We also give a technique to construct, for every n is an element of N, n algebraically independent everywhere surjective functions, f(1), f(2),..., f(n), so that for every non-constant polynomial P is an element of C[z(1), z(2),...,z(n)], P(f(1), f(2),...f(n)) is also everywhere surjective.