Eventually constant intertwining linear maps between complete locally convex spaces

Carlos Bosch, César L. García, Thomas E. Gilsdorf, Claudia Gómez-Wulschner, Rigoberto Vera

Research output: Contribution to journalArticlepeer-review


Starting from Sinclair’s 1976 work [6] 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.

Original languageEnglish
Pages (from-to)147-163
Number of pages17
JournalItalian Journal of Pure and Applied Mathematics
Issue number46
StatePublished - 2021


  • Gliding hump
  • Intertwining
  • Separating space


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