Unformatted text preview: Y is ±nitedimensional one can choose x so that d ( x,Y ) = 1. What if X is a Hilbert space ? (ii) Let X be an in±nite dimensional normed linear space. Show that there is a sequence { x n } ⊂ X satisfying b x b = 1 and b x n − x m b ≥ 1 for each n,m . (iii) Conclude that the closed unit ball is not compact if X is in±nitedimensional. 11 Luenberger Prob. 3.7 12 Luenberger Prob. 3.12 13 Luenberger Prob. 3.21 14 Luenberger Prob. 3.22...
View
Full Document
 Spring '08
 Staff
 Vector Space, Hilbert space, Compact space, normed linear space, Luenberger

Click to edit the document details