It is usually beneficial (to the viewers) to cinvert the image to sRGB -- this is like the lowest common denominator for monitors.
Not the space to use for prepress work, of course, but presenting small images on web pages is an entrely different business.
As to the perceived brightness, have a look at the intensity histogram. If there is some information above say RGB 240-245, these areas on the monitor should more or less pure white (or bright red, green, or blue; depending on the actual channel values). If they don't, your monitor is set too dark. RGB 245 should look different to RGB 255, if not, the monitor is too bright. On the other end of the scale, RGB 10+ should be visibly different and don't merge into featureless blacks. If not, your monitor is not bright enough. Then there is the old struggle of gamma wars between Macs and PCs which tend to be less important nowadays, but still using a very low or high gamma leads to viewing troubles for most users. Around 2.2 should be ideal.
The best is of course doing a hardware colour calibration with a dedicated device, no matter what colour space you end up with.
