Skip to main content\(\DeclareMathOperator{\dist}{dist}
\DeclareMathOperator{\Lim}{Lim^1}
\DeclareMathOperator{\diag}{diag}
\DeclareMathOperator{\trace}{Tr}
\DeclareMathOperator{\spans}{span}
\DeclareMathOperator{\spec}{\sigma}
\DeclareMathOperator{\essspec}{\sigma_{\mathrm{ess}}}
\DeclareMathOperator{\ind}{ind}
\newcommand{\Hil}{\mathcal{H}}
\newcommand{\vmid}{\,\middle\vert\,}
\renewcommand{\epsilon}{\varepsilon}
\renewcommand{\emptyset}{\varnothing}
\newcommand{\norm}[1]{\left\lVert #1 \right\rVert }
\newcommand{\abs}[1]{\left\lvert #1 \right\rvert}
\newcommand{\angles}[1]{\left\langle #1 \right\rangle}
\newcommand{\snorm}[1]{\lVert #1 \rVert }
\newcommand{\sabs}[1]{\lvert #1 \rvert}
\newcommand{\sangles}[1]{\langle #1 \rangle}
\newcommand{\lt}{<}
\newcommand{\gt}{>}
\newcommand{\amp}{&}
\)