The answer you need is to run your command as follows (or in a similar way):
sudo -u w3svcsadm bash -c 'echo "TEST ran" > /home/youribm/emaildigest/TEST_$( date +%Y%m%d%H%M%S ).output'
The difference is:
in your version, the sudo means that
echo "TEST ran" is being run as
> /home/youribm/emaildigest/TEST_$( date +%Y%m%d%H%M%S ).output is being run as your current user, which is apparently root.
what you actually want is for the whole block, including redirection, to be run as
w3svcsadm. In my suggestion, I achieve that by running
w3svcsadm, and telling
bash to run the full command-line (
echo "TEST ran" > /home/youribm/emaildigest/TEST_$( date +%Y%m%d%H%M%S ).output), and then exit.
Or, in simpler terms: redirection is a form of piping between two commands, and in your case, you want both commands to be run by the same user.
It may help to mentally replace
&&) to understand: command one is
echo, and command two is
write standard input into this file.
The first 'half' of the command (before redirection) is being run by sudo, and the rest is not.
Although we generally consider a command with output redirection as one command, it isn't - it is two commands, and so you need to ensure both commands are being run by the user you intended.