Projective limits of paratopological vector spaces
Alegre, Carmen
Bull. Belg. Math. Soc. Simon Stevin, Tome 11 (2005) no. 5, p. 83-93 / Harvested from Project Euclid
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In this paper we describe various methods of constructing new paratopological vector spaces from given ones. First, we introduce the notion of a right dual of a paratopological vector space with the aim to define a right weak topology. We prove that, in a certain class of normed spaces, the classical weak topology is determined by a right weak topology. Next, the quotient topology in the context of paratopological vector spaces is discussed. Finally, we consider the projective limit of paratopological vector spaces and prove that every pseudoconvex space is a projective limit of quasi-normed spaces.
Publié le : 2005-04-14
Classification:  paratopological vector space,  pseudoconvex,  quasi-norm,  continuous linear map,  right weak topology,  quotient topology,  projective limit,  46A03,  46A16,  54E35,  54H11 
@article{1113318132,
     author = {Alegre, Carmen},
     title = {Projective limits of paratopological vector spaces},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {11},
     number = {5},
     year = {2005},
     pages = { 83-93},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1113318132}
}

Alegre, Carmen. Projective limits of paratopological vector spaces. Bull. Belg. Math. Soc. Simon Stevin, Tome 11 (2005) no. 5, pp.  83-93. http://gdmltest.u-ga.fr/item/1113318132/