That has nothing to do with image resolution. Photoshop documents can only have one single resolution. What you are asking about is pixel dimensions. Yes, if you take a large and resize it to 1/2 its original size you are throwing away 1/2 of the pixels. If you do this in a document setup for 300 dpi or 75 dpi that layer like all of the layers will still be 300 dpi or 75 dpi or whatever you set it at when you created the document. If you resize that 1/2 size layer back to 100% size Photoshop has to guess at the new data being add. This works just like using Image Resize.
There is also a secondary problem with the transform tools. Photoshop at least CS2 and older has a rounding error. This means each time you use a transform tool like rotate, resize, etc. you are introducing errors in to the image data because of the round error in Photoshop. In fact this error can be used to create some interesting effects. Russell Brown who works for Adobe even created a script (doesn’t work with CS3 and he doesn’t plan to update it) that uses this flaw to create some very interesting effects. Because that script hasn’t been and won’t be updated for CS3 I don’t know if the round error has been fixed in CS3. Scratch that I just did a test and the rounding error is still there. I didn’t take it as far and Russell Brown’s script did but you can see what I mean here.
http://www.sonic.net/keesha/error.jpg This was done by rotating the image by 10 degrees about 20 to 30 times. Basically what this means is keep your transformations to a minimum as you are corrupting image data.
