Hi,

problem:If is an arbitrary sequence of complex numbers, and if is an element of , ,

write . Prove that is an element of and that ever element of can be obtained in this manner by a suitable choice of the 's

is the collection of all linear functionals on

attempt:To prove that is an element of I show that is a linear functional:

Prove that every element can be obtained in this manner by a suitable choice of the 's.

I am not sure how to prove this, but perhaps I can say that if the set of 's are a basis for , then every element of can be written as .

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Thanks!