Change displayed theorem numbering

The following solution is based on a straightforward adaptation of this answer by @egreg.

documentclass{article}
usepackage{amsthm}
%% Create a new theorem style called 'PlainNoDot':
newtheoremstyle{PlainNoDot}% name of the style to be used
  {topsep}% measure of space to leave above the theorem. E.g.: 3pt
  {topsep}% measure of space to leave below the theorem. E.g.: 3pt
  {itshape}% name of font to use in the body of the theorem
  {}% measure of space to indent
  {bfseries}% name of head font
  {}% punctuation between head and body: NONE <-- only diff. from default
  { }% space after theorem head; " " = normal interword space
  {thmname{#1}thmnumber{ #2}thmnote{ (#3)}}
%% Switch the active theorem style to 'PlainNoDot':
theoremstyle{PlainNoDot}
%% Start creating theorem-like environments:
newtheorem{theorem}{Theorem}[section]

begin{document}
setcounter{section}{2} % just for this example
begin{theorem} Bla bla bla. end{theorem}
end{document}