Coinbase is the only entity that knows the private keys which could be used to move the funds in this wallet. So if "owns" means actual technical control of the coins, Coinbase owns them.
Now, many people (pretty much all) follow the laws and contractual obligations of the region in which they live. Under the framework of that system, the funds at still belong to the customer that deposited them. Whether that means the customer "owns" them or is simply "owed" them by Coinbase is debatable...probably a pointless debate.
> Under the framework of that system, the funds at still belong to the customer that deposited them.
Careful. In the case of bankruptcy, you probably won't get your money back. Bloomberg Law[0]:
> An exchange going bankrupt would likely have to face Chapter 11 debtors’ rules on creditor recovery. Generally, secured creditors would be paid back first before others.
> A crypto exchange is not likely to have investor protection measures in place for cryptocurrency, though it could carry insurance policies for certain covered incidents, such as cybersecurity incident. And unless user terms specified otherwise, an investor would likely be an unsecured creditor who may not be able to recover what they’re owed.
