HDMI Splitter to Apple cinema display (model A1081) via DVI.

Hello all,

The output from my Mac goes into a HDMI splitter to feed my 22 inch HD television and my 20 inch Apple Cinema display (model A1081). Currently the splitter is working because it can feed the television, but I'm getting nothing on the cinema display. The splitter outputs HDMI, but its connected to my Cinema Display via a HDMI-DVI adapter.

Should this theoretically work, or is it a case of the monitor saying nono?

Thanks to anyone that could shed some light..