Bear in mind that "local $/..." will only be "local" if it's inside a curly-brace block:

{
   local $/=\"1024";
   open FILE, 'c:\space\sp.txt' or die $!;
   $_=<FILE>; #<IT WILL READ ONLY 1KB>
}
# now $/ is back to its original value

# another way (note that quotes are not needed):

open FILE, $name or die $!;
$_ = do { local $/ = \1024; <FILE> };
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If you miss that little detail, "local" is equivalent to "main".

But really, just using "read()" seems easier.