use strict;
use warnings;

use Regexp::Common;

my $str = "a<<a> a>b<a>c<a>a";
while ($str=~/\G(?:|$RE{balanced}{-parens=>'<>'})
                ([^<]+)
                (?:|$RE{balanced}{-parens=>'<>'})/xg)
{
 # Update: Oops, this uppercases everything except what
 # the OP wanted :)
 substr($str, $-[1],$+[1]-$-[1]) = uc $1;
 pos($str) = $+[1];
}