Linear subsets of nonlinear sets in topological vector spaces

For the last decade there has been a generalized trend in Mathematics on the search for large algebraic structures (linear spaces, closed subspaces, or infinitely generated algebras) composed of mathematical objects enjoying certain special properties. This trend has caught the eye of many researche...

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Detalles Bibliográficos
Autores: Bernal González, Luis, Pellegrino, Daniel M., Seoane Sepúlveda, Juan Benigno
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2014
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/87534
Acceso en línea:https://hdl.handle.net/11441/87534
https://doi.org/10.1090/S0273-0979-2013-01421-6
Access Level:acceso abierto
Palabra clave:Lineability
Spaceability
Algebrability
Real and complex analysis
Special functions
Operator theory
Baire category theorem
Hypercyclic manifolds
Zeros of polynomials
Descripción
Sumario:For the last decade there has been a generalized trend in Mathematics on the search for large algebraic structures (linear spaces, closed subspaces, or infinitely generated algebras) composed of mathematical objects enjoying certain special properties. This trend has caught the eye of many researchers and has also had a remarkable influence in Real and Complex Analysis, Operator Theory, Summability Theory, Polynomials in Banach spaces, Hypercyclicity and Chaos, and general Functional Analysis. This expository paper is devoted to providing an account on the advances and on the state of the art of this trend, nowadays known as lineability and spaceability.