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Lineability and algebrability of pathological phenomena in analysis

dc.contributor.authorGarcía-Pacheco, F.J.
dc.contributor.authorPalmberg, N.
dc.contributor.authorSeoane-Sepúlveda, Juan B.
dc.date.accessioned2023-06-20T10:33:09Z
dc.date.available2023-06-20T10:33:09Z
dc.date.issued2007
dc.description.abstractWe show that, in analysis, many pathological phenomena occur more often than one could expect, that is, in a linear or algebraic way. We show this by means of the construction of large algebraic structures (infinite dimensional vector spaces or infinitely generated algebras) enjoying some special or pathological properties.
dc.description.departmentDepto. de Análisis Matemático y Matemática Aplicada
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.facultyInstituto de Matemática Interdisciplinar (IMI)
dc.description.refereedTRUE
dc.description.sponsorshipAcademy of Finland
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/20079
dc.identifier.citationR.M. Aron, V.I. Gurariy, J.B. Seoane-Sepúlveda, Lineability and spaceability of sets of functions on R, Proc. Amer.Math. Soc. 133 (2005) 795–803. R.M. Aron, D. Pérez-García, J.B. Seoane-Sepúlveda,Algebrability of the set of non-convergent Fourier series, Studia Math., in press. R.M. Aron, J.B. Seoane-Sepúlveda, Algebrability of the set of everywhere surjective functions on C, Bull. Belg.Math. Soc. Simon Stevin, in press. R.P. Boas, A Primer of Real Functions, fourth ed., The Mathematical Association of America, 1996. P. Enflo, V.I. Gurariy, On lineability and spaceability of sets in function spaces, preprint. B.R. Gelbaum, J.M.H. Olmsted, Counterexamples in Analysis,Dover Publications, New York, 2003. V.I. Gurariy, Subspaces and bases in spaces of continuous functions, Dokl. Akad. Nauk SSSR 167 (1966) 971–973 (in Russian). H. Lebesgue, Leçons sur l’intégration, Gauthier–Willars,1904.
dc.identifier.doi10.1016/j.jmaa.2006.03.025
dc.identifier.issn0022-247X
dc.identifier.officialurlhttp://www.sciencedirect.com/science/article/pii/S0022247X06002745
dc.identifier.relatedurlhttp://www.sciencedirect.com
dc.identifier.urihttps://hdl.handle.net/20.500.14352/50465
dc.issue.number2
dc.journal.titleJournal of Mathematical Analysis and Applications
dc.language.isoeng
dc.page.final939
dc.page.initial929
dc.publisherElsevier
dc.relation.projectIDNo. 205644.
dc.rights.accessRightsrestricted access
dc.subject.cdu517.5
dc.subject.keywordAlgebrability
dc.subject.keywordSpaceability
dc.subject.keywordHamel basis
dc.subject.keywordTaylor expansion
dc.subject.keywordLinear functions
dc.subject.keywordR-linear functions
dc.subject.keywordDirichlet function
dc.subject.keywordEverywhere surjective functions
dc.subject.ucmFunciones (Matemáticas)
dc.subject.unesco1202 Análisis y Análisis Funcional
dc.titleLineability and algebrability of pathological phenomena in analysis
dc.typejournal article
dc.volume.number326
dspace.entity.typePublication
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