map has two syntax:
map BLOCK LIST
map EXPR, LIST
Perl must determine which syntax you are using. The problem is that both BLOCK and EXPR can start with { because { ... } can be the hash constructor (e.g. my $h = { a => 1, b => 2 };).
That means that Perl's grammar is ambiguous. When an ambiguity is encountered, perl guesses what you mean after looking ahead a little. In your situation, it guessed wrong. It guessed { was the start of a hash constructor instead of the start of a block. You will need to disambiguate explicitly.
The following are convenient ways to disambiguate blocks and hash constructors:
+{ ... }   # Not a valid block, so must be a hash constructor.
{; ... }   # Perl looks head, and sees that this must be a block.
So in your case, you could use
my %b = map {; "number $_" => 2*$_ } @a;
Related: Difference between returning +{} or {} in perl from a function, and return ref or value