Hi I am trying to prove the following, but I am getting absolutely nowhere: {δ_k }_(k=1)^∞ is an orthonormal basis for L^2 (N),where δ_k is the sequence in L^2 (N) whose kth entry is 1. Thanks in advance [/FONT]
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Originally Posted by Ase Hi I am trying to prove the following, but I am getting absolutely nowhere: {δ_k }_(k=1)^∞ is an orthonormal basis for L^2 (N),where δ_k is the sequence in L^2 (N) whose kth entry is 1. Thanks in advance [/FONT] and all other entries are 0. The inner product defined on , the space of square summable sequences (also called ), is so you need to show three things: 1) That is a basis for 2) That for all k 3) That if
if if GTM 233 page 332
Thanks a lot HallsofIvy. I will get at it right away and hopefully crack it.
Hey, The sequence is also a basis for the normed vector space . Couldn't you show that for any there exists unique scalars such that ?
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