You don't need to read the content into a scalar then split it. Instead, directly assign to an array, like the documentation of Net::OpenSSH shows:

my @df_arr = $ssh->capture("df -k /home/ | tail -1") or die "Unable to
+ run command\n";
print "$s:  Disk space /home/ = $df_arr[3] \n";
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I find it very confusing if you name a variable $fh when it is not a filehandle.

If you want to make your code more concise, consider the introduction of different routines which return information given a server connection:

sub disk_space {
    my( $ssh, $dir ) = @_;
    my @df_arr = $ssh->capture("df -k '$dir' | tail -1") or die "Unabl
+e to run command\n";
    print "Disk space $dir = $df_arr[3]\n";
}

disk_space( $ssh, '/home/' );
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