推 herstein:利用內積的連續性 01/06 11:41
※ 編輯: Jer1983 來自: 140.136.133.8 (01/06 13:08)
推 dorminia:如果你已經算出(x+z,y)=(x,y)+(z,y), 用連續逼近就好辦 01/06 15:06
→ ntust661:強! 01/06 15:14
※ 編輯: Jer1983 來自: 140.136.133.8 (01/06 15:30)
Suppose ( X , ||.|| ) is a normed linear space and
||x+y||^2 +||x-y||^2 = 2 * ( ||x||^2 + ||y||^2 ).
Define (x,y) = (1/4) * ( ||x+y||^2 - ||x-y||^2 )
Show that (x,y) is an inner product.
其他的部分已經證完了
剩下 (ax,y) = a(x,y), a is scalar 的部份不知道從何著手
thanks in advance.
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我證到最後一步了 (ax,y) = a(x,y) for a = integers, rationals, and -1
最後 for a in |R, choose r_n in Q such that r_n -> a
therefore, (r_nx,y) = r_n(x,y) and then taking limit on both sides
lim (r_nx,y) = lim r_n (x,y) = a(x,y)
^^^^^^^^^^^^ **********************
這邊要用什麼性質才能得到lim (r_nx,y) = (ax,y) ? 打*號的部分應該是ok吧?
麻煩大家了 謝謝
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