I hope to draw the following diagram
Thanks a lot for your help.
The purpose of this site is to help you when you got stuck trying something, not to convert screen shots into LaTeX code.
\documentclass{article}
\usepackage{tikz-cd}
\begin{document}
\[\begin{tikzcd}
\mathcal{H} \arrow[d,"W_A" swap] \arrow[r,"T"]& \mathcal{H} \arrow[d,"W_A"] \\
\mathbf{R}(A^{1/2}) \arrow[r,"T" swap] & \mathbf{R}(A^{1/2})\\
\end{tikzcd}\]
\end{document}
\begin{tikzcd}by e.g. \begin{tikzcd}[sep=huge].
–
Jan 10 '19 at 18:58
Similar output of the great user @marmot using an alternative xy package from this guide XY-pic.
\documentclass[a4paper,12pt]{article}
\usepackage[all,cmtip]{xy}
\begin{document}
\xymatrix{
\mathcal{H} \ar[d]_{W_A} \ar[r]^T
& \mathcal{H} \ar[d]^{W_A}\\
\mathbf{R}(A^{1/2}) \ar[r]^{\tilde T} & \mathbf{R}(A^{1/2})}
\end{document}
Obligatory tikzcd editor answer: https://tikzcd.yichuanshen.de/
Click the screenshot to open in the editor.
Generated code by clicking the {} button (not an MWE):
\begin{tikzcd}
\mathcal{H} \arrow[rr, "T"] \arrow[d, "W_A"'] & & \mathcal{H} \arrow[d, "W_A"] \\
\mathbf{R}(A^{1/2}) \arrow[rr, "\tilde{T}"] & & \mathbf{R}(A^{1/2})
\end{tikzcd}
tikz-cdmanual you will find it straightforward to draw this. – Jan 10 '19 at 18:43