Try this:

#!/usr/bin/perl

use strict;

# create data structure
my $LOG = {};
$LOG->{A} = [];

# $LOG->{A}[0] is the same as $LOG->{A}->[0]
#              is the same as $$LOG{A}->[0]

# create anonymous file handle
$LOG->{A}[0] = do { local *FH };

# open file for writing, assign to anon file handle
open($LOG->{A}[0], ">dummy.txt") || 
    die "Unable to open test file.";

# unable to print directly to the pointer, so we select it instead
select($LOG->{A}[0]);

print <<EOF;
    This is a test of the anonymous file handle procedure. 
    Were this an actual, real-life procedure, instructions 
    would follow this message.
EOF

# we're done, go ahead and close the sucker
close($LOG->{A}[0]);
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Ya with me? :)