The notion of functions dependent locally on finitely many coordinates plays an important role in the theory of smoothness and renormings on Banach spaces, especially when higher order smoothness is involved. In this note we investigate the structural properties of Banach spaces admitting (arbitrary) bump functions depending locally on finitely many coordinates.
It is proved that every locally inner derivation on a symmetric norm ideal of operators is an inner derivation.
Let be a locally A-pseudoconvex algebra over or . We define a new topology on which is the weakest among all m-pseudoconvex topologies on stronger than . We describe a family of non-homogeneous seminorms on which defines the topology .
The aim of this paper is to study the relationships between the concepts of local near uniform smoothness and the properties H and H*.
Let be a completely regular Hausdorff space and a real normed space. We examine the general properties of locally solid topologies on the space of all -valued continuous and bounded functions from into . The mutual relationship between locally solid topologies on and
Locally solid topologies on vector valued function spaces are studied. The relationship between the solid and topological structures of such spaces is examined.