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The space D ( U ) is not B r -complete

Manuel Valdivia (1977)

Annales de l'institut Fourier

Certain classes of locally convex space having non complete separated quotients are studied and consequently results about B r -completeness are obtained. In particular the space of L. Schwartz D ( Ω ) is not B r -complete where Ω denotes a non-empty open set of the euclidean space R m .

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

Taras Banakh (2000)

Studia Mathematica

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 ∞ = l i m 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...

Triebel-Lizorkin spaces on spaces of homogeneous type

Y.-S. Han (1994)

Studia Mathematica

In [HS] the Besov and Triebel-Lizorkin spaces on spaces of homogeneous type were introduced. In this paper, the Triebel-Lizorkin spaces on spaces of homogeneous type are generalized to the case where p 0 < p ≤ 1 ≤ q < ∞ , and a new atomic decomposition for these spaces is obtained. As a consequence, we give the Littlewood-Paley characterization of Hardy spaces on spaces of homogeneous type which were introduced by the maximal function characterization in [MS2].

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