KSH: define a variable in for loop with the loop counter (syntax issue)

Question

#!/bin/ksh
today=$(date "+%b %e")
homedir=/home/

for dir in jim bob joe; do
    rootfiles_today_[$dir]=$(ssh hostname "ls -lrt $homedir$dir" | grep root | grep "$today")
    printf "\n root owns the following files in $dir "
    printf "\n\tSize\tDate\tTime\tFile Name\n\n"
    printf "$rootfiles_today_[dir]" | awk '{printf "\t" $5 "\t" $6 " " $7 "\t" $8 "\t" $9 "\n"}'
done

When I try this, the output gives me

rootfiles_today_jim=: not found

as if the variable name is keeping hold of the = instead of using it to define the variable. I can't get past this part, each variation involving quotes, [], {}, set -A, eval, (ksh88 does not have define) that i can think of either doesn't work and stops the script, or gives the same above.

How can I properly define the (dynamic? iterative? I don't know the correct term) variable name or persuade it to let the = do its job?

Secondarily, please confirm my way to call the variable once defined is going to be ${rootfiles_today_[dir]} inside the loop? What about after the loop is over, if I want to add more to the script and have these 3 vars i can call by name, I will have to either call by their specific full name or echo $@ | grep word to call a specific one, or (I am fumbling this question, I know there are many ways to do almost anything) is there another way to call one or all of them iteratively if needed in a subsequent loop? This is more of a secondary ask, the main issue is getting a useful variable defined.

All of this is simpler in Bash and newer shells, my main stumbling blocks tend to be things that are different or limited in ksh.