Should the alpha channel be gamma corrected We know that in PNG,BMP,etc... the pixel value stored is not in the linear RGB space. But I found no document saying anything about the alpha channel. Is the alpha channel stored in image files in linear space or not?
We know that in PNG,BMP,etc... the pixel value stored is not in the linear RGB space.


This is not necessarily true. You can store whatever color space you want into an image, it doesn't even need to be colors (such as normal maps).

The alpha channel is generally linear. The alpha channel doesn't get displayed, but it is generally a non-color term used for transparency (or whatever else). Because they don't need to display on a monitor, there's no reason to store in in gamma space. If you did, you would unnecessarily lose precision at the lower end of the alpha values. Normals maps follow a similar line of reasoning, as explained very well by Julien Guertault.