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The symbiosis of C*- and W*-algebras

These days it is common for young operator algebraists to know a lot about C*-algebras, or a lot about von Neumann algebras -- but not both. Though a natural consequence of the breadth and depth of each subject, this is unfortunate as the interplay between the two theories has deep historical roots and has led to many beautiful results. We review some of these connections, in the context of amenability, with the hope of convincing (younger) readers that tribalism impedes progress.