I have question about the operator space theory. How to solve equation (2.2.1) in details
Note that for any $a\in M_n(V)$, $$ \varphi_{n+1}\left( \begin{pmatrix} a & 0 \\ 0 & 0\end{pmatrix} \right) = \varphi_n(a) $$ And $$ \left\|\begin{pmatrix} a & 0 \\ 0 & 0\end{pmatrix}\right\|_{M_{n+1}(V)} = \|a\|_{M_n(V)} $$ Does this help?
Copyright © 2021 JogjaFile Inc.
Note that for any $a\in M_n(V)$, $$ \varphi_{n+1}\left( \begin{pmatrix} a & 0 \\ 0 & 0\end{pmatrix} \right) = \varphi_n(a) $$ And $$ \left\|\begin{pmatrix} a & 0 \\ 0 & 0\end{pmatrix}\right\|_{M_{n+1}(V)} = \|a\|_{M_n(V)} $$ Does this help?