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Linear subsets of nonlinear sets in topological vector spaces



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Bernal González, Luis and Pellegrino, Daniel and Seoane-Sepúlveda, Juan B. (2014) Linear subsets of nonlinear sets in topological vector spaces. Bulletin of the American Mathematical Society, 51 (1). pp. 71-130. ISSN 0273-0979

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Official URL: http://www.ams.org/journals/bull/2014-51-01/S0273-0979-2013-01421-6/S0273-0979-2013-01421-6.pdf


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.

Item Type:Article
Uncontrolled Keywords:Lineability; spaceability; algebrability; real and complex analysis; special functions; operator theory; Baire category theorem; hypercyclic manifolds; zeros of polynomials
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:24002
Deposited On:19 Dec 2013 10:16
Last Modified:28 Nov 2016 09:39

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