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 in my mind. All the text about process address space and virtual memory layout mentions that the process address space has space reserved for kernel. For e.g. on 32 bit systems the process address space is 4GB of which 1 GB is reserved for kernel in Linux (Might be different on other OS).
I am just wondering why kernel is said to be in the process address space when a process cannot address the kernel directly. Why don't we say that the kernel has a separate address space than a process and why can't we have a different page table for kernel itself which is separate from the page tables of the processes?
Can I get an explanation with respect to Linux (Debian or Ubuntu) specific operating system?