The talk will start with a non-technical introduction to operator algebraic semicontinuity and show the relationship to operator convexity and strong operator convexity. By looking at one special situation, it is possible to show the main ideas without using any operator theory, and this will be emphasized. Thus people who know some basic things about bounded linear operators on Hilbert space, but don't know anything about operator algebras, will still be able to understand most of the talk.