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Thank you Nick. If it's not too much trouble, could you say a few words about the "getting a new , different weak $^{*}$ topology" part of your answer? How would you use $T$ to get that new topology?
Thank you Nick, I actually think I got it in a different way. It is easy to show that T is adjointable, which implies is weak$^{*}$ continuous. By the way, how is the map $T_{*}$ between the preduals defined?
