A Corda network is a set of well identified legal entities. When you want to join a network you sign a legal document (participation terms of use) and then you submit something called Certificate Signing Request; once it's approved your node automatically downloads the required certificates that identify it on that network and allows it to become discoverable by other nodes so it can interact with them.
Corda network is an example, and I recommend that you go through their website: https://corda.network
In the case of Corda network, the operator is a consortium; not one organization.
That link I shared, will answer all of your questions:
- Participation: https://corda.network/participation/index
- Governance: https://corda.network/governance/index
- Types of networks in Corda network: https://corda.network/participation/network-choice
- Notary: https://corda.network/participation/notary-considerations