American Airlines famously killed upstart after upstart that attempted to fly out of Dallas Love Field. They kept a lease on two gates, but left them unused almost all of the time (AA generally flies out of the larger Dallas-Fort Worth International Airport). Whenever any new company tried to start new service out of Love field, American would open those two gates, match routes exactly to the startup, and charge substantially less, clearly incurring a loss for each plane flown. As soon as the new company was driven into bankruptcy, AA would again shutter those gates, leaving them available to crush the next company that tried to start at Love Field. See, e.g., Legend Airlines.

Right, so then the startup should sell nonrefundable tickets several weeks in advance. As soon as American starts flying those routes below cost, move your own planes to a different route, book all your passengers with nonrefundable tickets on the American flights and pocket the difference. As soon as they stop, start flying those routes again.

There is presumably some regulatory burden preventing someone from doing this. Maybe you can't move planes from one route to another so easily etc. But then that's how the company does it. Without that method of forcing the new competitor to incur unrecoverable costs, they can't do it.

It's theoretically possible to have a natural market barrier like that, but in practice to be a barrier that large it's nearly always a regulatory compliance issue. The law says you can't sign up customers on long-term contracts, preventing new competitors from locking in customers at the current price rather than the below-cost price. The law says an ISP has to serve the whole city and not just one neighborhood, increasing the startup capital required by a factor of a hundred. The law prohibits adversarial interoperability, so you can't distribute your own apps unless you can manufacture your own phones.

Most monopolies don't come from natural causes.

Can you imagine how furious people would be if they found out their airline put them on their cheaper competitor's flights and kept the difference? Rationality be damned, they'd be out for blood. I can hear the screaming already. Good luck.

This happens every day.

Really? How do I learn more about this?

Codeshare agreements, for example British Airways sells Vueling (budget airline) flights under BA flight numbers.