Let E be a locally convex linear Hausdorff topological space which is angelic when furnished with the weak topology, and let C be a closed convex subset of E with x0 ∈ C. Suppose F : C → K(C) is a weakly sequentially upper semicontinuous map with the following properties holding...
In this paper, the notion of weakly equicompact set is used to obtain characterizations of spaces X such that X negated left arrow l(1), of spaces X such that B-X* is weak* sequentially compact and also to obtain several results concerning to the weak operator and the strong operator ...
We define Xη as the set of all non-decreasing functions φ∈X such that 0≤φ(s)≤η(s) for all s∈S. Note that each φ∈Xη is upper semicontinuous. Observe that 0 is a continuity point of every function φ∈Xη. Proposition 1 The set Xη is convex and sequentially compact ...
If $X$ is not weakly sequentially complete, then relatively weakly compact subsets need not be $\\\beta\\\sb1$-equicontinuous. Even if $X$ is weak... Gruenwald,M Edward - 《Dissertation Abstracts International》 被引量: 7发表: 1989年 Nonlinear weakly sequentially continuous embeddings between...
In this paper, the notion of weakly equicompact set is used to obtain characterizations of spaces X such that X ↩̸ ℓ1, of spaces X such that B X* is weak* sequentially compact and also to obtain several results concerning to the weak operator and the strong operator topologies. ...
Fréchet, a continuous and bounded function f mapping + to E is said to be asymptotically almost periodic if the set of all translates of f by elements of + is relatively compact in C b ( + ,E). This paper investigates strongly continuous groups and semigroups T of operators on E for...
Observe that 0 is a continuity point of every function \varphi \in X^\eta . Proposition 1 The set X^\eta is convex and sequentially compact in X. Proof It is obvious that X^\eta is convex. For any f\in X^\eta and m\in \mathbb { N}, we define the function f^m as follows:...