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

@article{Banakh2000,
abstract = {We show that the strong dual X’ to an infinite-dimensional nuclear (LF)-space is homeomorphic to one of the spaces: $ℝ^ω$, $ℝ^∞$, $Q×ℝ^∞$, $ℝ^ω×ℝ^∞$, or $(ℝ^∞)^ω$, where $ℝ^∞ = lim ℝ^n$ and $Q=[-1,1]^ω$. In particular, the Schwartz space D’ of distributions is homeomorphic to $(ℝ^∞)^ω$. 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 $ℝ^∞$ or to $Q×ℝ^∞$. In particular, the strong dual to any metrizable infinite-dimensional Montel space is homeomorphic either to $ℝ^∞$ or to $Q×ℝ^∞$.},
author = {Banakh, Taras},
journal = {Studia Mathematica},
keywords = {dual space; nuclear (LF)-space; Montel space; direct limit; Hilbert cube; nuclear LF space; strong dual space},
language = {eng},
number = {3},
pages = {201-208},
title = {Topological classification of strong duals to nuclear (LF)-spaces},
url = {http://eudml.org/doc/216699},
volume = {138},
year = {2000},
}

TY - JOUR
AU - Banakh, Taras
TI - Topological classification of strong duals to nuclear (LF)-spaces
JO - Studia Mathematica
PY - 2000
VL - 138
IS - 3
SP - 201
EP - 208
AB - We show that the strong dual X’ to an infinite-dimensional nuclear (LF)-space is homeomorphic to one of the spaces: $ℝ^ω$, $ℝ^∞$, $Q×ℝ^∞$, $ℝ^ω×ℝ^∞$, or $(ℝ^∞)^ω$, where $ℝ^∞ = lim ℝ^n$ and $Q=[-1,1]^ω$. In particular, the Schwartz space D’ of distributions is homeomorphic to $(ℝ^∞)^ω$. 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 $ℝ^∞$ or to $Q×ℝ^∞$. In particular, the strong dual to any metrizable infinite-dimensional Montel space is homeomorphic either to $ℝ^∞$ or to $Q×ℝ^∞$.
LA - eng
KW - dual space; nuclear (LF)-space; Montel space; direct limit; Hilbert cube; nuclear LF space; strong dual space
UR - http://eudml.org/doc/216699
ER -