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Possible Duplicate:
Question about Fredholm operator

This seems to be a standard result but I cannot find the solution. Let $M:X \rightarrow U$ be a bounded linear map between two Banach spaces. Assume that the range is a finite -codimensional subspace of U; then the range is closed.

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    See [this post](http://math.stackexchange.com/questions/146723/question-about-fredholm-operator) for a solution.2012-11-29
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    But here we dont have $Ker(M)$ with finite dimension @DavidMitra2012-11-29
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    @Tomás I linked the wrong post. It's corrected now; point 3. of t.b.'s answer is relevant.2012-11-29
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    Yes @DavidMitra, the answer is there.2012-11-29

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