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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

 

Linear subsets of nonlinear sets in topological vector spaces


Authors: Luis Bernal-González, Daniel Pellegrino and Juan B. Seoane-Sepúlveda
Journal: Bull. Amer. Math. Soc. 51 (2014), 71-130
MSC (2010): Primary 15A03, 46E10, 46E15; Secondary 26B05, 28A20, 47A16, 47L05
Published electronically: July 15, 2013
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Abstract: 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.


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Additional Information

Luis Bernal-González
Affiliation: Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, Apdo. 1160, Avenida Reina Mercedes, Sevilla, 41080, Spain
Email: lbernal@us.es

Daniel Pellegrino
Affiliation: Departamento de Matemática, Universidade Federal da Paraíba, 58.051-900 - João Pessoa, Brazil
Email: pellegrino@pq.cnpq.br; dmpellegrino@gmail.com

Juan B. Seoane-Sepúlveda
Affiliation: Departamento de Análisis Matemático, Facultad de Ciencias Matemáticas, Plaza de Ciencias 3, Universidad Complutense de Madrid, Madrid, 28040, Spain
Email: jseoane@mat.ucm.es

DOI: http://dx.doi.org/10.1090/S0273-0979-2013-01421-6
PII: S 0273-0979(2013)01421-6
Keywords: Lineability, spaceability, algebrability, real and complex analysis, special functions, operator theory, Baire category theorem, hypercyclic manifolds, zeros of polynomials
Received by editor(s): November 26, 2012
Received by editor(s) in revised form: April 2, 2013
Published electronically: July 15, 2013
Additional Notes: The first author was partially supported by Ministerio de Economía y Competitividad Grant MTM2012-34847-C02-01
The second author was supported by INCT-Matemática, CAPES-NF, CNPq Grants 301237/2009-3 and 477124/2012-7
The third author was supported by MTM2012-34341
Article copyright: © Copyright 2013 American Mathematical Society