How is the lightning network secured against hacking and double spends? As I understand payment-channels, like the lightning network, they are working off chain (no record in the blockchain). The only record to the blockchain is the deposit transaction to open the payment-channel and by closing the payment channel. But later all the transactions inside the payment-channel running on centralized servers, like traditional bank transfers. This is very fast, and could be very cheap if there is competition. But how the banks, who would run such payment-channels can secure that inside the payment-channel the transactions are not hacked and safe? And how the bank guarantee the customers that they dont double spend the funds if inside the channel all transaction are totally anonymous?
All transactions that are sent between the two parties in a channel are valid bitcoin transactions, and they can be used to close the channel at any time by either party. 

When a channel is opened, those bitcoins are locked up in that channel until it is closed with a spending transaction, sending an agreed amount of bitcoin to each party in the channel. Initially this spending transaction is created to return the same amount of bitcoin that each party put in to the channel. But 'transactions' are made, which is really just each party agreeing to create new spending transactions to replace the old one, giving each party a different amount. 

If each party, for example, locks in 1 BTC to a channel, they will also create a spending transaction at the same time returning that 1 BTC to each person. Then let's say person A wants to send 0.2 BTC to person B. To do this, they simply work together to create a new valid spending transaction to replace the old one, the new one would pay A 0.8 BTC and B 1.2 BTC, effectively transferring that 0.2 BTC from A to B. New transactions like this are continually created every time either person wants to send coins, until finally one of the two participants wishes to close the channel and actually get their BTC back. This also happens if one party stops responding/cooperating. The final transaction they agreed upon is broadcast to the actual blockchain, closing the channel and paying both participants.

Thus, at all times, the transactions are valid and the actual bitcoins being exchanged are locked up in the blockchain, so there is no way for anyone to double-spend the transactions.