I've *always* used that definition of OS--software that operates hardware.
That is why I have such a difficult time accepting that MS was allowed to get away with claiming that IE is part of the OS--it controls no hardware. Other applications as well should not be included. The OS should be merely a collection of drivers and firmware that controls access to the hardware.
Nothing more.
OK, then you are an exception because most conversations regarding this are almost never based on that. When is the last time someone bought a kernel for their computer? Or asked what kernel version is on your phone?
Well, "hardware" and critical system resources both hard and virtual. Thus, time/task scheduling, system resource management and allocation, and a few other core functions belong in the OS too, even though not strictly "hardware"...
But certainly, nothing as far up the chain as communications, file system, compression/encryption, god forbid the freakin' web browser.