On completely continuous operators on locally convex vector spaces

Notes on Locally Convex Topological Vector Spaces

Notes from a 1994–95 graduate course. Designed to supplement the topological vector space chapters of Rudin's Functional Analysis.

On Some Approximation Theorems for Power q-Bounded Operators on Locally Convex Vector Spaces

This paper deals with the study of some operator inequalities involving the power q-bounded operators along with the most known properties and results, in the more general framework of locally convex vector spaces.

Completely Continuous Multilinear Operators on C(k) Spaces

Given a k-linear operator T from a product of C(K) spaces into a Banach space X, our main result proves the equivalence between T being completely continuous, T having an X-valued separately ω∗ − ω∗ continuous extension to the product of the biduals and T having a regular associated polymeasure. It is well known that, in the linear case, these are also equivalent to T being weakly compact, and ...

Banach Algebras of Operators on Locally Convex Spaces

Hyperinvariant Subspaces for Some Operators on Locally Convex Spaces

Some results concerning hyperinvariant subspaces of some operators on locally convex spaces are considered. Denseness of a class of operators which have a hyperinvariant subspace in the algebra of locally bounded operators is proved.