Topological classification of strong duals to nuclear (LF)-spaces

Banakh, Taras

Banakh, Taras

Studia Mathematica, Tome 141 (2000), p. 201-208 / Harvested from The Polish Digital Mathematics Library

Résumé

We show that the strong dual X’ to an infinite-dimensional nuclear (LF)-space is homeomorphic to one of the spaces: $ℝ^{ω}$ , $ℝ^{\infty}$ , $Q \times ℝ^{\infty}$ , $ℝ^{ω} \times ℝ^{\infty}$ , or ${(ℝ^{\infty})}^{ω}$ , where $ℝ^{\infty} = l i m ℝ^{n}$ and $Q = {[- 1, 1]}^{ω}$ . In particular, the Schwartz space D’ of distributions is homeomorphic to ${(ℝ^{\infty})}^{ω}$ . As a by-product of the proof we deduce that each infinite-dimensional locally convex space which is a direct limit of metrizable compacta is homeomorphic either to $ℝ^{\infty}$ or to $Q \times ℝ^{\infty}$ . In particular, the strong dual to any metrizable infinite-dimensional Montel space is homeomorphic either to $ℝ^{\infty}$ or to $Q \times ℝ^{\infty}$ .

Publié le : 2000-01-01

Zbl 0952.57006

EUDML-ID : urn:eudml:doc:216699

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     author = {Taras Banakh},
     title = {Topological classification of strong duals to nuclear (LF)-spaces},
     journal = {Studia Mathematica},
     volume = {141},
     year = {2000},
     pages = {201-208},
     zbl = {0952.57006},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv138i3p201bwm}
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Banakh, Taras. Topological classification of strong duals to nuclear (LF)-spaces. Studia Mathematica, Tome 141 (2000) pp. 201-208. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv138i3p201bwm/

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