[vetinari]

Currently not, but nothing prevents Amazon from implementing it. It is actually very simple, when the user clicks on Install button on the Android Market web, it then sends c2dm [1] message to your device and the localy installed Android Market app pulls the installation file.

Amazon is free to do the same thing.

[1] http://code.google.com/android/c2dm/index.html

[ydant]

One small clarification - Amazon is free to do part of the process (download it automatically), but Amazon cannot install the application automatically on most phones. The actual installation step requires privileges that the Amazon Market app doesn't have access to (but the Android Market app does).

Of course, custom Amazon Android devices won't have that restriction.