The latex classes use ‘\@sec’ and ‘\@ssect’ for defining sections and starred sections. The ams classes use only the first feature for both types of classes, but assume negative depth \@m for the depth of starred sections (tex4ht records the level value in \c:secnumdepth). Hence, the ‘like’ versions of the sectioning comamnds are (currently?) not provided for the ams classes. The \Configure{@sec @ssect} is needed only for the @sec; a configuration for @ssect is ignored.
<..sections of amsart.cls..>
<.ams art + book + proc.>
<.ams art + proc.>
<.ams no@sect.>
-_-_-
<..sections of amsbook.cls..>
<.ams art + book + proc.>
<.chapters for book / report.>
<.ams no@sect.>
-_-_-
<..sections of amsproc.cls..>
<.ams art + book + proc.>
<.ams art + proc.>
<.ams no@sect.>
-_-_-
<..ams no@sect..>
\def\no@sect#1#2#3#4#5#6[#7]#8{%
\edef\@toclevel{\ifnum#2=\@m 0\else\number#2\fi}%
\ifnum #2>\c@secnumdepth \let\@secnumber\@empty
\else \@xp\let\@xp\@secnumber\csname the#1\endcsname
\refstepcounter{#1}\fi
\let\@svsec=\empty
\let\@svsechd=\empty
\global\@nobreaktrue
\@xsect{#5}}
\let\@ssect=\relax
-_-_-
<..ams art + proc..>+
\let\no@part=\part
\Def:Section\part{\ifnum \c:secnumdepth>\c@secnumdepth \else
\thepart \fi}{#1}
\let\no:part=\part
\def\part{\rdef:sec{part}}
-_-_-
<..ams book..>+
\let\:tempb\part
\Def:Section\part{\ifnum \c@secnumdepth >-2 \the\c@part\fi}{#1}
\let\:part\part
\let\part\:tempb
\let\no@part\@part
\def\@part[#1]#2{%
\gdef\c:secnumdepth{-2}%
\ifnum \c@secnumdepth >-2\relax \refstepcounter{part}\fi
\HtmlEnv \Toc:Title{#1}\:part{#2}}
\Def:Section\likepart{}{#1}
\let\:likepart\likepart
\let\likepart\:UnDef
\let\no@spart\@spart
\def\@spart#1{\HtmlEnv \:likepart{#1}}
-_-_-
<..ams divisions..>
\let\no@section=\section
\Def:Section\section{\ifnum \c:secnumdepth>\c@secnumdepth \else
\thesection \fi}{#1}
\let\no:section=\section
\def\section{\rdef:sec{section}}
-_-_-
<..ams divisions..>+
\let\no@subsection=\subsection
\Def:Section\subsection{\ifnum \c:secnumdepth>\c@secnumdepth \else
\thesubsection \fi}{#1}
\let\no:subsection=\subsection
\def\subsection{\rdef:sec{subsection}}
-_-_-
<..ams divisions..>+
\let\no@subsubsection=\subsubsection
\Def:Section\subsubsection{\ifnum \c:secnumdepth>\c@secnumdepth \else
\thesubsubsection \fi}{#1}
\let\no:subsubsection=\subsubsection
\def\subsubsection{\rdef:sec{subsubsection}}
-_-_-
<..ams divisions..>+
\let\no@paragraph=\paragraph
\Def:Section\paragraph{\ifnum \c:secnumdepth>\c@secnumdepth \else
\theparagraph \fi}{#1}
\let\no:paragraph=\paragraph
\def\paragraph{\rdef:sec{paragraph}}
-_-_-
<..ams divisions..>+
\let\no@subparagraph=\subparagraph
\Def:Section\subparagraph{\ifnum \c:secnumdepth>\c@secnumdepth \else
\thesubparagraph \fi}{#1}
\let\no:subparagraph=\subparagraph
\def\subparagraph{\rdef:sec{subparagraph}}
-_-_-
<..ams art, proc, book..>+
\pend:defI\@seccntformat{%
\def\@secnumpunct{\ifnum \c:secnumdepth>0
\expandafter\ifx\csname the##1\endcsname\relax \else. \fi\fi}}
-_-_-