Results 1 to 10 of about 38 (31)
Some remarks about Mackey convergence
International Journal of Mathematics and Mathematical Sciences, 1995 In this paper, we examine Mackey convergence with respect to K-convergence and bornological (Hausdorff locally convex) spaces. In particular, we prove that: Mackey convergence and local completeness imply property K; there are spaces having K- convergent
Józef Burzyk, Thomas E. Gilsdorf
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Fast complete locally convex linear topological spaces
International Journal of Mathematics and Mathematical Sciences, 1986 This is a study of relationship between the concepts of Mackey, ultrabornological, bornological, barrelled, and infrabarrelled spaces and the concept of fast completeness. An example of a fast complete but not sequentially complete space is presented.
Carlos Bosch +2 more
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Barrelled and Bornological Function Spaces
Journal of Mathematical Analysis and Applications, 2000 A subset \(K\) of a completely regular topological space \(Y\) is \(t\)-bounded if \(f(K)\) is a bounded subset of \(\mathbb{R}\) for every real continuous function \(f\) on \(Y\). Let \(X\) be a completely regular topological space. \(\nu X\) is the real-compactification of \(X\).
Vesko Valov
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A class of bornological barrelled spaces which are not ultrabornological
Mathematische Annalen, 1971 N. Bourbaki, [1, p. 35], notices that it is not known if every bornological barrelled space is ultrabornological. In this paper we prove that if E is the topological product of an infinite family of bornological barrelled spaces, of non-zero dimension, there exists an infinite number of bornological barrelled subspaces ofE, which are not ...
Valdívia Manuel
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A class of quasi-barrelled (DF)-spaces which are not bornological
Mathematische Zeitschrift, 1974 Manuel Valdívia
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Convolution on distribution spaces characterized by regularization
Mathematische Nachrichten, Volume 296, Issue 5, Page 1938-1963, May 2023., 2023 Abstract Locally convex convolutor spaces are studied which consist of those distributions that define a continuous convolution operator mapping from the space of test functions into a given locally convex lattice of measures. The convolutor spaces are endowed with the topology of uniform convergence on bounded sets.
Tillmann Kleiner, Rudolf Hilfer
wiley +1 more source
Wave Front Sets with respect to the Iterates of an Operator with Constant Coefficients
Abstract and Applied Analysis, Volume 2014, Issue 1, 2014., 2014 We introduce the wave front set WF*P(u) with respect to the iterates of a hypoelliptic linear partial differential operator with constant coefficients of a classical distribution u ∈ 𝒟′(Ω) in an open set Ω in the setting of ultradifferentiable classes of Braun, Meise, and Taylor.
C. Boiti +3 more
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Buchwalter‐Schmets theorems and linear topologies
International Journal of Mathematics and Mathematical Sciences, Volume 22, Issue 1, Page 13-16, 1999., 1999 In this paper, we obtain Buchwalter‐Schmets theorems in the realm of Lefschetz linearly topologized spaces.
L. M. Sánchez Ruiz, J. R. Ferrer
wiley +1 more source
Mackey convergence and quasi‐sequentially webbed spaces
International Journal of Mathematics and Mathematical Sciences, Volume 14, Issue 1, Page 17-26, 1991., 1991 The problem of characterizing those locally convex spaces satisfying the Mackey convergence condition is still open. Recently in [4], a partial description was given using compatible webs. In this paper, those results are extended by using quasi‐sequentially webbed spaces (see Definition 1).
Thomas E. Gilsdorf
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International Journal of Mathematics and Mathematical Sciences, Volume 4, Issue 1, Page 39-53, 1981., 1981 A Mazur space is a locally convex topological vector space X such that every fϵXs is continuous where Xs is the set of sequentially continuous linear functionals on X; Xs is studied when X is of the form C(H), H a topological space, and when X is the weak * dual of a locally convex space. This leads to a new classification of compact T2 spaces H, those
Albert Wilansky
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