Maybe your code should look somewhat like

#!/usr/bin/perl

my ($file1,$file2);
open(FILE1,"<$ARGV[0]");

while(<FILE1>)
{
   chomp($_);
   $file1 = $_;
   $file1=~s/\s+//;
   open(FILE2,"<$ARGV[1]");
   while(<FILE2>)
   {
      print "<$file1> \n";
   }
   close FILE2;
}
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?

What output do you wish or expect?