Remove period at the end of section numbers in amsart

documentclass{amsart}
makeatletter
def@seccntformat#1{%
  protecttextup{protect@secnumfont
    csname the#1endcsname
%%%    protect@secnumpunct
space
  }%
}


renewcommand{tocsection}[3]{%
  indentlabel{@ifnotempty{#2}{ignorespaces#1 #2%.
     quad}}#3}
lettocsubsectiontocsection
lettocsubsubsectiontocsection

makeatother
begin{document}
tableofcontents

section{$leftarrow$ I'd like to remove this period}

subsection{$leftarrow$ And this one too}

subsubsection{$leftarrow$ This one as well}

end{document}