Let $X $ be a Banach space and $X^* $ its dual space. Let $\{x_n\} $ be a sequence that converges weakly to $x\in X $, and $\{f_n\}\subset X^* $ a sequence that converges in the strong topology of $X^*$. Show that $$(x_n,f_n)\to (x,f).$$ I didn't manage to give a precise meaning to $(\cdot ,\cdot) $: can you tell me what does this notation stand for? (I didn't find anything in Wikipedia) Thanks
2026-04-15 13:11:20.1776258680
Notation question (regarding weak topology / dual spaces)
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