Unfortunately, I have to work with Mackey Topology on a topological group under the duality theory. My primary reference is Topological Vector Space, but it is concise. I have searched for literature; it is scattered and seems not so much. I am interested in completeness, compactness, and, most importantly, Dunford-Pettis properties. Any help is needed.
2026-04-03 22:29:55.1775255395
Reference recommendation: Mackey Topological in terms of Compactness and Completeness and Dunford-Pettis on Topological groups
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Köthe's Toplogical Vector Spaces I is a pretty good book, where $\S21$ seems to cover the Mackey topology fairly well. It is a little old though and I doubt it covers anything on Dunford-Pettis.
Bogachev is another good author for these kinds of things, so you could try Topological Vector Spaces and Their Applications by him and Smolyanov though you might find some of the results you are interested in relegated to the exercises.
I don't have it to hand to check, but I also seem to recall Treves's Topological Vector Spaces being comprehensive, so assuming you're checking all these in a library, that might also be worth a look.