Infinitely many local minima of sequentially weakly lower semicontinuous functionals

A minimax theorem in infinite-dimensional topological vector spaces

In this paper, we obtain a minimax theorem by means of which, in turn, we prove the following result: Let $E$ be an infinite-dimensional reflexive real Banach space, $T:E\to E$ a non-zero compact linear operator, $φ:E\to {\bf R}$ a lower semicontinuous, convex and coercive functional, $I\subset {\bf R}$ a compact interval, with $0\in I$, $ψ:I\to {\bf R}$ a lower semicontinuous convex function. Then, for each $r>φ(0)$, one has $$\sup_{x\in X}\inf_{λ\in I}(φ(T(x)-λx)+ψ(λ))=r+ψ(0)\ ,$$ where $$X=\{x\in E : φ(T(x))\leq r\}\ .$$

The Pelczynski property for tight subspaces

We show that if X is a tight subspace of C(K) then X has the Pelczynski property and X^* is weakly sequentially complete. We apply this result to the space U of uniformly convergent Taylor series on the unit circle and using a minimal amount of Fourier theory prove a theorem of Bourgain, namely that U has the Pelczynski property and U^* is weakly sequentially complete. Using separate methods, we prove U and U^* have the Dunford-Pettis property. Some results concerning pointwise bounded approximation are proved for tight uniform algebras. We use tightness and the Pelczynski property sto make a …

拟伪度量空间中的强Ekeland变分原理

The strong Ekeland variational principle in quasi-pseudometric spaces

本文旨在将Georgiev和Suzuki版本的强Ekeland变分原理推广到拟伪度量空间，并探讨其向非对称赋范空间推广的可能性。