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Cascales, Kąkol, Saxon proved [3] that in a large class $$ E \in \mathfrak{G} $$ of locally convex spaces (lcs) (containing ( LM)-spaces and ( DF)-spaces) for a lcs $$ \mathfrak{G} $$ the weak topology σ ( E,E′) of E has countable tightness iff its weak dual ( E′, σ( E′,E)) is K-analytic. Applying examples of Pol [9] (and Kunen [12]) one gets that there exist Banach spaces C( X) over a compact...
This survey paper collects some of older and quite new concepts and results from descriptive set topology applied to study certain infinite-dimensional topological vector spaces appearing in Functional Analysis, including Fréchet spaces, (LF)-spaces, and their duals, (DF)-spaces and spaces of continuous real-valued functions C(X) on a completely regular Hausdorff space X. Especially (LF)-spaces and...
We present criteria for determining mean ergodicity of C0-semigroups of linear operators in a sequentially complete, locally convex Hausdorff space X. A characterization of reflexivity of certain spaces X with a basis via mean ergodicity of equicontinuous C0-semigroups acting in X is also presented. Special results become available in Grothendieck spaces with the Dunford–Pettis property.
Clayton, Schottenloher and Mujica have reduced the study of the Michael problem to certain specific algebras of holomorphic functions on infinite dimensional spaces. In this note we establish a general theorem that yields as special cases the aforementioned results.
A counterpart of the Mackey–Arens Theorem for the class of locally quasi-convex topological Abelian groups (LQC-groups) was initiated in Chasco et al. (Stud Math 132(3):257–284, 1999). Several authors have been interested in the problems posed there and have done clarifying contributions, although the main question of that source remains open. Some differences between the Mackey Theory for locally...
A deep result of $$C_{p}$$ C p -theory, due to D. P. Baturov, states that if X is a Lindelöf $$\Sigma $$ Σ -space, for every subset H of $$C_{p}\left( X\right) $$ C p X the extent of H equals the Lindelöf number of H. The most useful consequence of this result asserts that if X is a Lindelöf $$ \Sigma $$ Σ -space, every countably compact subset H of $$C_{p}\left(...
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