my $inp = 'AAA * BBB CCC * * "2000 01 00 00 00" "2004 01 00 00 00"' ;

my @r;
while ($inp =~ /(
                    [^"\s]+
                |
                    "[^"]+?"
                )
                /gx) {
    my $a = $1;
    $a =~ s/(?:^"|"$)//g;
    push @r, $a;
}

print join "\n", @r, '';
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Do you really not want to match AAA? I assumed you want AAA in there; if not, shift @r or something. This solution isn't the most efficient, but I think it's clear enough to expand upon (or abandon in favor of Text::CSV_XS).