Tough analysis question

Let B denote the complex Banach space dual of littleL^2.
That is, B: = B(littleL^2, C), the space of linear maps from littleL^2
into C, complex numbers.
The norm on B is the usual operator norm.

Let f: littleL^2 -> C be a bounded linear function

(That is, f /in B).

Prove that there exists a sequence in littleL^2 (y_n) such that for
all sequences (x_n),

f maps (x_n) |-> sigma(n=1 to infinity) x_n * conjugate(y_n)
.

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