Home Work (5) Let I be a normed space, I is its olual. bet F=1&i xe &}, where ? It defined by ?(). 1f1x)/, f 1*. show th

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Home Work 5 Let I Be A Normed Space I Is Its Olual Bet F 1 I Xe Where It Defined By 1f1x F 1 Show Th 1 (58.27 KiB) Viewed 28 times

Home Work (5) Let I be a normed space, I is its olual. bet F=1&i xe &}, where ? It defined by ?(). 1f1x)/, f 1*. show the following: (i) { is a semi-norm, for each x + 1 lü) the family & separrakes the points of I. (in) i V(x, P. P , E), XE L P E F 1 knym, &? is a base for a topology on Ih (denoked by ) (iv) The topology 6(**) on I* Homsdorff The mapping (62) fg and (7,flif are o(It I) - Continuous That is (It, 6(2, 2)) is a linent topological spale (vid ( 1 , 6(808)) is locally convex speaker .') 678*7) jou (6)