RT Journal Article
T1 Lineability and algebrability of pathological phenomena in analysis
A1 García-Pacheco, F.J.
A1 Palmberg, N.
A1 Seoane-Sepúlveda, Juan B.
AB We 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.
PB Elsevier
SN 0022-247X
YR 2007
FD 2007
LK https://hdl.handle.net/20.500.14352/50465
UL https://hdl.handle.net/20.500.14352/50465
LA eng
NO R.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.
NO Academy of Finland
DS Docta Complutense
RD 27 jul 2024