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# 数学final代考 Math 328 & Math 601代写 Math代写

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## Math 328 & Math 601

### Directions:数学final代考

Open this booklet only when directed to do so.

Check that you have all 7 pages including this one.

You may use the backs of sheets for rough work, or if you need additional space for your answer.

Each question is worth 16 points. (Total: 100 points)

No cheating sheets may be used.

This examination is two days (48 hours) in duration.

### 4. 数学final代考

Determine whether the following statements true or false. Give reasons.

(a) Every bounded sequence in Rn has a convergent subsequence.

(b) The dual space of (Rn, ∥· 1) is (Rn, ∥· 1).

(c) In a Hilbert space, every bounded sequence has a convergent subsequence.

### 5.

Suppose that the sequence (xn)n∈N in H satisfies

(a) There exists M > 0 such that for every n N, ∥ xn ≤ M.

(b) For every y M, limn xn, y〉exists.

(c) M is total in H.

Prove that for every y ∈ H, limn xn, y exists.

The prev:

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