Closed range for maps between banach spaces?

Asked Nov 29 '12 at 15:23

Active Nov 29 '12 at 15:23

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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.

edited Apr 13 '17 at 12:21

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asked Nov 29 '12 at 15:23

Johan

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See this post for a solution. – David Mitra Nov 29 '12 at 15:59
But here we dont have $Ker(M)$ with finite dimension @DavidMitra – Tomás Nov 29 '12 at 16:05
@Tomás I linked the wrong post. It's corrected now; point 3. of t.b.'s answer is relevant. – David Mitra Nov 29 '12 at 16:13
Yes @DavidMitra, the answer is there. – Tomás Nov 29 '12 at 16:32

Closed range for maps between banach spaces?

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