This is a question to elaborate on this one: Why is kernel said to be in process address space?
This might be a silly question but it just popped up i
A process "owns" the entire virtual address space here, the kernel and the user portions of it.
Its inability to peek and poke the kernel code and data is not due to different address spaces, it's due to different access rights/permissions set in the page tables. Kernel pages are set up in such a way that regular applications can't access them.
It is, however, customary to refer to the two parts of one whole thing as the kernel space and the user space and that can be confusing.