Run apps with redirection from within a shell script

I have a watchdog script that runs applications listed in a file. I want to be able to run the applications as entered in that file. Currently I am just looping thru the file and running them in the background if there is no pid associated with those apps, I simply run app with (list_Entry &) to allow all arguments that app might have and redirections of I/O intact. While arguments are working properly, its not working for the listEntry that looks like "my_app >> /tmp/mylog.txt 2>&1", the redirection argument doesn't create a /tmp/mylog, instead stdout gets routed to my script. How can I prevent this from hapening?

while true
do
  test /mnt/appsList && {
    input="/mnt/appsList"
    while IFS= read -r line
    do
    if echo $line | grep -q  "^[a-z/(]"; then
      app_base=$(basename `echo "$line"|cut -f1 -d ' '|tr -d [:space:]`)
      #echo "testing run status for $app_base"
      pid_app=$(pgrep -f $app_base)
      # echo "`date` : pid of $app_base is $pid_app" | tee -a  $_SYS_LOG_DIR/system_log

      if [ -z "$pid_app" ];then
         echo "`date` : Running $line " | tee -a  $_SYS_LOG_DIR/system_log
         ($line) &
         sleep 10
      fi
    fi
    done < "$input"
  }
sleep 5
done

Thanks Ratin