Art:
Moria's suggestion will do somewhat what you are looking for, but there will be much distortion (i.e. the type towards the left and right ends of the text will lean like a bunch of palm trees in florida in june).
The way I prefer to do this (I'll put together a small toot tomorrow), is to:
1. Type your text;
2. Draw a rectangle, roughly the width and tallest height of your desired text warp. Leave selected;
2. Object>Gradient Mesh>Make, set for 1 row, 2 columns;
3. Select text and gradient mesh, then hit Ctrl-Alt-C (Object>Envelope>Make with Top Object), and now your text is inside an envelope;
4. With the direct selection tool (white arrow, no +), grab the center bottom anchor. Drag it STRAIGHT up (Hold Shift while dragging. If it's not dead straight, you will get undesireable distortions. Drag it up to the tallest point on the desired arc, where the text has to be narrowest;
5. The bottom half now looks like a mirrored grand piano set. Select one of the corner anchors, and look at where its horizontal handle lies. Drag it straight up, so the arc follows until you have a nice arc on that side. If you wish (for symmetry purposes) you can drag a guide to the handle, so you can line up the other corner handle exactly like it. Or, just eyeball it.
HTH
Bert