Connect Sony Laptop with HDMI (and VGA but not DVI) to Sony 23" Cinema HD display (DVI only) at 1920 x 1200 - dvi to vga connects for cinema hd display for macs

I my new Sony laptop and my Apple Cinema Display 23 "(native resolution of 1920 x 1200 DVI) as a second monitor.

My laptop is a VGNFZ28G (with HDMI and VGA, and an NVIDIA ® GeForce ® 8600M GS GPU).

Can I simply use a DVI-HDMI adapter to extend my screen on my monitor at its native resolution? Are there any side effects?

I also have the Belkin docking attempt, but it can only turn DVI 1600 x 1200 (not 1920 x 1200 I'm looking) - Are there alternatives to this resolution?