3

I'm facing difficulties in compilation

    \documentclass[12pt,a4paper]{report}
    \usepackage{amssymb,amsmath,amsthm,mathrsfs}
      \usepackage{mathtools, nccmath}

    \begin{document}
     Let $\mathbf{T} = (T_1,\cdots,T_d)\in \mathcal{B}(\mathcal{H })^d$. The joint maximal numerical range  of $\mathbf{T}$ denoted $JtW_{\max}(\mathbf{T})$, is defined as
   \begin{align*}
     JtW_{\max}(\mathbf{T})
     & = \left\{(\lambda_1,\cdots,\lambda_d)\in \mathbb{C}^d;\;\exists\, 
     (x_n)_n\subset 
      \mathcal{H}\,;\;\;\|x_n\|=1,\displaystyle\lim_{n\to+\infty}\langle T_k 
      x_n\mid x_n\rangle=\lambda_k,\\
     & \text{and}\;\displaystyle\lim_{n\to+\infty}\|T_kx_n\|=\|T_k\|,\; 
       1\leq k \leq d\;\right\}.
    \end{align*}
      \end{document} 

My goal is to get

enter image description here

  • A serious issue with the screenshot you posted is that the first line is wider than the textblock. – Mico Dec 16 '18 at 13:00
  • 2
  • @albert - It's not a duplicate: a main issue with the current query is that one of the lines is wider than the text block, making it impossible to center both lines. – Mico Dec 16 '18 at 13:08
  • 1
    you should also remove the \displaystyle (which do nothing there as align uses displaystyle anyway, but in other places would make an odd layout with half the expression on in textstyle and half in display (it applies to the whole expression not just the \lim) – David Carlisle Dec 16 '18 at 13:17
  • @mico thanks. OP: question should probably be posed a bit more clearly, regarding error message, and header etc. – albert Dec 16 '18 at 13:23
7

The main issue with your code is that it's not permissible to split the scope of \left and \right across two or more lines. Another issue is that the first line in the screenshot you posted is wider than the texblock.

I'd use a multline* environment instead of an align* environment, and I'd move \lim_{n\to+\infty}\langle T_k x_n\mid x_n\rangle=\lambda_k from the first line to the second.

Incidentally, both \displaystyle directives are redundant. And, you should be using \dots (or \ldots) rather than \cdots in two places.

enter image description here

\documentclass[12pt,a4paper]{report}
\usepackage{amssymb,amsthm,mathrsfs,mathtools,nccmath}
\newcommand\jtw{\mathit{Jt\!W}}
\newcommand\jtwmax{\jtw_{\!\!\max}}

\begin{document}
Let $\mathbf{T}=(T_1,\dots,T_d)\in\mathcal{B}(\mathcal{H})^d$. The joint maximal 
numerical range  of $\mathbf{T}$, denoted $\jtwmax(\mathbf{T})$, is defined as
\begin{multline*}
     \jtwmax(\mathbf{T})= \bigl\{
     (\lambda_1,\dots,\lambda_d)\in \mathbb{C}^d; 
     \ \exists\, (x_n)_n\subset\mathcal{H};
     \ \|x_n\|=1, \\
     \lim_{n\to\infty}\langle T_k x_n\mid x_n\rangle=\lambda_k 
     \text{ and }
     \lim_{n\to\infty}\|T_kx_n\|=\|T_k\|,\ 1\leq k \leq d \bigr\}.
\end{multline*}
\end{document} 
  • Thank you for your great answer. Just I hope to know what is the difference between \left \right and \bigr? Thanks. – Schüler Dec 16 '18 at 17:01
  • @Schüler - \left and \right are for automatic sizing of round parentheses, square brackets, curly braces, and all other (mathematical) "fences". As noted earlier, \left and \right must not occur on different lines; that's why you can't use them for the two-line formula at hand. \bigl\{ and \big\} increase the sizes of the curly braces by fixed amount. (Other fixed-amount sizing instructions are \Big, \bigg, and \Bigg.) The formula doesn't require anything bigger than \big (pun intended). – Mico Dec 16 '18 at 17:14
  • I poste a similar question with 4 equations. Can I use multine? – Schüler Jan 16 at 15:49
  • \begin{multline*} W_{\max}^A(T) =\{\lambda\in \mathbb{C}\,;\;\; \exists\,(b_n)_n\subset\overline{\mathcal{R}(A)}\,;\;\;\|b_n\|_A=1,\displaystyle\lim_{n\to+\infty}\langle T b_n\mid b_n\rangle_A=\lambda,\\ \text{and}\;\displaystyle\lim_{n\to+\infty}\|Tb_n\|_A=\|T\|_A\;\}\\ =\{\lambda\in \mathbb{C}\,;\;\; \exists\,(b_n)_n\subset\overline{\mathcal{R}(A)}\,;\;\;\|b_n\|_A=1,\displaystyle\lim_{n\to+\infty}\langle PT b_n\mid b_n\rangle_A=\lambda,\\ \text{and}\;\displaystyle\lim_{n\to+\infty}\| PTb_n\|_A=\|PT|_{\overline{\mathcal{R}(A)}}\|_A\;\}=W_{\max}^{A_0}(T_0), \end{multline*} – Schüler Jan 16 at 15:49
  • However the = are not in the same signs. Thank you for the help. – Schüler Jan 16 at 15:50

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