Consider the R-vector space 8. le (R) :=D {(zn) C R; Σ < oo} n=0 of square summable reell sequences, endowed with the norm (호:) 1/2 n=0 Show that dB1,(®) (0, 1) = {(xn) e 2(R); ||(xn)||12(R) = 1} is closed and bounded, but not compact. Hint: Investigate the sequence (en), where en is the sequence whose n-th element is 1 and all others 0.

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