Icahn has built his reputation over the years as a corporate raider and activist shareholder, pressuring companies to change their business strategies and boost their stocks. JetBlue and Spirit have both asked for an expedited appeal of the judge's recent decision, with a U.S. appeals court set to hear arguments in June. But some analysts say the chances of a successful appeal are low. JetBlue's new CEO, Joanna Geraghty, has vowed "aggressive action" to return the airline to profitability.