A noncompact Choquet theorem
A normability condition on locally convex spaces.
In a previous work (1990) we introduced a certain property (y) on locally convex spaces and used it to remove the assumption of separability from the theorem of Bellenot and Dubinsky on the existence of nuclear Köthe quotients of Fréchet spaces. Our purpose is to examine condition (y) further and relate it to some other normability conditions. Some of our results were already announced in Önal (1989).
A note on a theorem of Klee
It is proved that if are separable quasi-Banach spaces, then contains a dense dual-separating subspace if either or has this property.
A Note on B- and Br-Completeness.
A note on Banach spaces without the approximation property
A Note on B-Complete Spaces and the Closed Graph Theorem.
A note on closed graph theorems.
A Note on compactness in Banach spaces.
A note on direct sum of ordered topological vector spaces
A note on embedding into product spaces
Using factorization properties of an operator ideal over a Banach space, it is shown how to embed a locally convex space from the corresponding Grothendieck space ideal into a suitable power of , thus achieving a unified treatment of several embedding theorems involving certain classes of locally convex spaces.
A note on extreme contractions on -spaces
A Note on Extreme Positive Definite Matrices.
A note on Fréchet-Urysohn locally convex spaces.
Recently Cascales, Kąkol and Saxon showed that in a large class of locally convex spaces (so called class G) every Fréchet-Urysohn space is metrizable. Since there exist (under Martin’s axiom) nonmetrizable separable Fréchet-Urysohn spaces Cp(X) and only metrizable spaces Cp(X) belong to class G, we study another sufficient conditions for Fréchet-Urysohn locally convex spaces to be metrizable.
A note on -spaces.
A note on implicit functions in locally convex spaces.
A note on infinite dimensional convex sets.
A note on intersections of simplices
We provide a corrected proof of [1, Théorème 9] stating that any metrizable infinite-dimensional simplex is affinely homeomorphic to the intersection of a decreasing sequence of Bauer simplices.
A note on Kakutani type fixed point theorems.
A note on L-Dunford-Pettis sets in a topological dual Banach space
The present paper is devoted to some applications of the notion of L-Dunford-Pettis sets to several classes of operators on Banach lattices. More precisely, we establish some characterizations of weak Dunford-Pettis, Dunford-Pettis completely continuous, and weak almost Dunford-Pettis operators. Next, we study the relationships between L-Dunford-Pettis, and Dunford-Pettis (relatively compact) sets in topological dual Banach spaces.
A Note on Locally Convex Spaces.