Boundedness and surjectivity in normed spaces

Boundedness and Surjectivity in Normed Spaces

We define the (w∗-) boundedness property and the (w∗-) surjectivity property for sets in normed spaces. We show that these properties are pairwise equivalent in complete normed spaces by characterizing them in terms of a category-like property called (w∗-) thickness. We give examples of interesting sets having or not having these properties. In particular, we prove that the tensor product of tw...

The Uniform Boundedness Theorem in Asymmetric Normed Spaces

and Applied Analysis 3 The condition of right K-completeness for X, p leaves outside the scope of this theorem an important class of asymmetric normed spaces, the asymmetric normed spaces associated to normed lattices because these spaces are right K-complete only for the trivial case 13 . In this paper, we give a uniform boundedness type theorem in the setting of asymmetric normed spaces which...

D-boundedness and D-compactness in finite dimensional probabilistic normed spaces

In this paper, we prove that in a finite dimensional probabilistic normed space, every two probabilistic norms are equivalent and we study the notion of Dcompactness and D-boundedness in probabilistic normed spaces.

Remotality and proximinality in normed linear spaces

In this paper, we consider the concepts farthest points and nearest points in normed linear spaces, We obtain a necessary and coecient conditions for proximinal, Chebyshev, remotal and uniquely remotal subsets in normed linear spaces. Also, we consider -remotality, -proximinality, coproximinality and co-remotality.

-approximation in normed spaces