As an Operation Owner, you have the following permissions for inviting new members :
Operation-specific: You can invite other users to join your assigned department (For Example if you are the Operation Owner for Op1, you can invite another Operation Owner to control the same).
Hierarchical Control: You can assign new members as Process Owners within your Operation.
Limitations: You cannot invite users to Operations that you do not own. For example if you are the Operation Owner for Op1, you cannot invite user to other Operations such as Op2 and Op3 mapped to your account.