In WCG Banach spaces, Gamma-convergence of convex lsc functions in the norm topology is equivalent to Gamma-convergence of their Fenchel conjugates in the weak* topology and to graphical convergence of the subdifferentials, under equicoercivity.
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Gamma-Convergence of Convex Functions, Conjugates, and Subdifferentials
In WCG Banach spaces, Gamma-convergence of convex lsc functions in the norm topology is equivalent to Gamma-convergence of their Fenchel conjugates in the weak* topology and to graphical convergence of the subdifferentials, under equicoercivity.