Activist investors like Carl C. Icahn and William A. Ackman know how to rattle the cages of Corporate America’s chief executives. These so-called corporate raiders have long been storming onto boards in the broader market, threatening proxy fights and demanding that management make changes, from spinning off divisions to putting an entire blue-chip company on the block. But recently such activists have started shaking up real estate investment trusts. Equity REITs own pools of properties, ranging from apartment buildings to shopping malls, which are packaged up as vehicles for investment. Under REIT rules, companies avoid paying corporate taxes by distributing at least 90 percent of their income as dividends to shareholders. Some REITs are public, while others are nontraded private REITs. Some major retailers and restaurants, like Sears and Darden Restaurants, have adopted the REIT strategy by spinning off their properties into separately traded REITs to raise cash.