The Minimal Context for Local Boundedness in Topological Vector Spaces

The local boundedness of classes of operators is analyzed on different subsets directly related to the Fitzpatrick function associated to an operator. Characterizations of the topological vector spaces for which that local boundedness holds is given in terms of the uniform boundedness principle. For example the local boundedness of a maximal monotone operator on the algebraic interior of its domain convex hull is a characteristic of barreled locally convex spaces.