@Anonymous
You cannot utilize a view on a SharePoint list at this time. However, you can certainly put that same logic into a Filter in PowerApps.
You didn't mention any criteria information or columns in your lists, so, as an example:
Filter(projectList, projectOwner=User().DisplayName)
This would, if used as a datasource for a Gallery, give you a list of all the items in projectList that have a column called projectOwner set to the display name of the current user.
If you have more specifics you need some help with, post back and we'll go further on it.
I hope this is helpful for you.