Characterizations of continuity
Suppose that $${\displaystyle F:X\to Y}$$ is a linear operator between two topological vector … See more

Every linear functional on a topological vector space (TVS) is a linear operator so all of the properties described above for continuous linear operators apply to them. However, because of their specialized nature, we can say even more about continuous linear … See more

• Bounded linear operator – Linear transformation between topological vector spaces
• Compact operator – Type of continuous linear operator
• Continuous linear extension – Mathematical … See more

Throughout, $${\displaystyle F:X\to Y}$$ is a linear map between topological vector spaces (TVSs).
Bounded subset
The notion of a "bounded set" for a topological vector space is that of being a von Neumann … See more

A locally convex metrizable topological vector space is normable if and only if every bounded linear functional on it is continuous.
A continuous linear … See more