My kitchen looks out onto an airwell, so it is always dark and depressing inside. Besides turning on the lights, is there any way to brighten the space?

You need to reflect as much daylight into the kitchen as possible. Going with an all-white kitchen is an obvious choice. You can also increase reflected light by painting a large section of the wall opposite the kitchen window in metallic silver, or paneling the backsplash in mirror-finished stainless steel.

Shiny doesn't have to mean tacky. Look for pearlised stone or man-made worktops and cabinet door fronts with metal laminate in a corrugated pattern. The textured surfaces will reflect more light than a smooth one. Finish the look with steel rails and handles.