[分析] 實變sequential convergene/compactness
1. Let 1<p<∞ and f_0 belong to L^p(R). For each natural number n, define
f_n(x)=f_0(x-n) for all x. Define f=0 on R. Show that {f_n}-->f in L^p(R). Is
this true for p=1?
2. Let [a,b] be a nondegenerate closed, bounded interval. In the Banach space
C[a,b], normed by the maximum norm, find a bounded sequence that fails to
have any strongly convergent subsequence.
感謝各位實變高手能給我一些解答或方向!
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