If I understand correctly, you want a separate array to be created for each input file. The following code creates a hash of array references, with the key being the file name and the value a reference to an array containing all the lines that do not begin with '>':

my %results;
{ local @ARGV =  ( 'q1.fa', 'q2.fa' );
  /^>/ or push @{ $results{ $ARGV } }, $_ while <>;
}
[download]

To access (ie print) this HoA, you could do, for example:

for ( keys %results ) {
  print "$_:\n";
  print @{ $results{ $_ } };
  print "\n";
}
[download]