Put the two cups of water and the sugar in a pan and heat over low heat, while stirring occasionally until the sugar dissolves.
Bring up the heat so the liquid comes to a boil and remove from the heat immediately. Let cool to room temperature, cover the pan and place in the refrigerator.
Use a glass bowl in which to mix together the strawberry and banana purees, 2/3 cup water, lemon juice and corn syrup. Stir it well, then place in the refrigerator for at least two hours.
When ready to make the sorbet, blend the cold sugar mixture into the fruit mixture. Pour this combined mixture into the type of ice cream maker you like best and produce the sorbet.
Once you have the frozen sorbet, place it into a glass bowl, cover it and freeze for at least 8 hours. This will make more than a quart of sorbet, which can be served using an ice cream dipper or spoon (dipped in water before each scoop to keep it from sticking).
Readers with questions or comments for Dave Kessler may write to him in care of this publication.