Question

Find a sequence which converges to 0 but is not in any space lp

Answer 1

Answer:

I am studying functional analysis and I have a problem about finding a sequence converging to zero such that this sequence is not in lp for every p. By lp I mean

lp={(xk)=(x1,x12,...):Σ|xk|p<∞}

where 1<p<∞. First I thought very simple sequence i/k which converges to zero but then I realized when p>2 it is element of lp space. I thought couple more examples but they did not work either. Can somebody help me out here?

Thanks.