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Unformatted text preview: l q , then X i =1  i  i   x  p  y  q . 1 6. Note: this is nitedimensional! Given the Holder inequality: if p,q > 0 satisfy 1 p + 1 q = 1 and x = { 1 , 2 , , n } l p , y = { 1 , 2 , , n } l q , then n X i =1  i  i   x  p  y  q , prove the Minkowski inequality  x + y  p  x  p +  y  p . 7. Prove that every convergent sequence is a Cauchy sequence. 8. Note: this is nitedimensional! Prove that the space of sequences x = { 1 , , n } , with the norm  x  = ( n X i =1  i  p ) 1 p , is a Banach space. 2...
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 Fall '09
 Math

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