\newcommand*{\kp}[2]{ {#1}\odot{#2} }
% The adjoint of a linear operator.
-\newcommand*{\adjoint}[1]{ {#1}^{*} }
+\newcommand*{\adjoint}[1]{ #1^{*} }
% The ``span of'' operator. The name \span is already taken.
\newcommand*{\spanof}[1]{ \operatorname{span}\of{{#1}} }