The local equicontinuity of a maximal monotone operator

Abstract

The local equicontinuity of an operator $T:X\rightrightarrows X^{*}$ with proper Fitzpatrick function $\varphi_{T}$ and defined in a barreled locally convex space $X$ has been shown to hold on the algebraic interior of $\operatorname*{Pr}\,_{X}(\operatorname*{dom}\varphi_{T})$). The current note presents direct consequences of the aforementioned result with regard to the local equicontinuity of a maximal monotone operator defined in a barreled locally convex space.