Another way to go using rubasov's data set plus a completely illegal line (ZA). The below is more "wordy" than other solutions, but I think what it does and how it does it is clear. If for example, RESULT=" " should be disallowed, there is a clear place to do that modification.

#!/usr/bin/perl -w
use strict;

while (<DATA>) 
{
   chomp;
   my $result = is_match($_);
   defined($result) ? print "$_:\tRESULT=\"$result\"\n"
                    : print "$_:\tRESULT=NO MATCH\n";
}

sub is_match
{
   my $term = shift;
   my $inner = ($term =~ m/^A(.*)Z$/)[0];
   return undef  if (!defined($inner));
   return $inner if $inner eq "";
   return $inner if $inner =~ m/^\s/;
   return undef;
}

=prints:
AZ:    RESULT=""
AZZ:    RESULT=NO MATCH
A SOMETHING Z:    RESULT=" SOMETHING "
ASOMETHINGZ:    RESULT=NO MATCH
A  Z:    RESULT="  "
A ZZ:    RESULT=" Z"
AAZZ:    RESULT=NO MATCH
AA ZZ:    RESULT=NO MATCH
ZA:    RESULT=NO MATCH
=cut

__DATA__
AZ
AZZ
A SOMETHING Z
ASOMETHINGZ
A  Z
A ZZ
AAZZ
AA ZZ
ZA
[download]

Update: I looked at the OP's spec again and it appears that this tweaking of is_match() would be better?:

sub is_match
{
   my $term = shift;
   my $inner = ($term =~ m/^A(.*)Z$/)[0];
   return undef  if (!defined($inner));
   return undef  if $inner eq "";
   return $inner if $inner =~ m/^\s+\S/;
   return undef;
}
prints:.....
AZ:    RESULT=NO MATCH
AZZ:    RESULT=NO MATCH
A SOMETHING Z:    RESULT=" SOMETHING "
ASOMETHINGZ:    RESULT=NO MATCH
A  Z:    RESULT=NO MATCH
A ZZ:    RESULT=" Z"
AAZZ:    RESULT=NO MATCH
AA ZZ:    RESULT=NO MATCH
ZA:    RESULT=NO MATCH
[download]