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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...
It is an open problem if any separable compact space K whose function space C(K) with the cylindrical σ-algebra is a standard measurable space, embeds in the space of the first Baire class functions on the Cantor set, with the pointwise topology. We prove that this is true for separable linearly ordered compacta. Other problems discussed in this note concern the Borel structures in C(K) generated...
Given a bounded linear operator S on a real Banach space X, we characterize weak topological transitivity of the operator families $${\lbrace S^t \mid t \in {\mathbb N}\rbrace}$$ , $${\lbrace \kappa S^t\mid\, t \in {\mathbb N},\, \kappa >0 \rbrace}$$ , and $${\lbrace \kappa S^t\mid\, t \in {\mathbb N},\, \kappa \in {\mathbb R}\rbrace}$$ in terms of the point spectrum of the dual operator...
For a compact space K we denote by $$C_w(K)$$ C w ( K ) ( $$C_p(K)$$ C p ( K ) ) the space of continuous real-valued functions on K endowed with the weak (pointwise) topology. In this paper we address the following basic question which seems to be open: Suppose that K is an infinite (metrizable) compact space. Can $$C_w(K)$$ C w ( K ) and $$C_p(K)$$ ...
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