Starting from Sinclair’s 1976 work  on automatic continuity of linear operators on Banach spaces, we prove that sequences of intertwining continuous linear maps are eventually constant with respect to the separating space of a fixed linear map. Our proof uses a gliding hump argument. We also consider aspects of continuity of linear functions between locally convex spaces and prove that such a linear function T from the locally convex space X to the locally convex space Y is continuous whenever the separating space G(T) is the zero vector in Y and for which X and Y satisfy conditions for a closed graph theorem.
|Number of pages||17|
|Journal||Italian Journal of Pure and Applied Mathematics|
|State||Published - 2021|
- Gliding hump
- Separating space