An estimate of the depth from an intermediate subfactor (Q1894317)

Summary: We show that for a triple \(K\subset N\subset M\) of type \(\text{II}_1\) factors the depth of the inclusion ``\(K\subset M\)'' is not greater than the maximum of depths of the inclusions ``\(K\subset N\)'' and ``\(N\subset M\)'', provided there is such a factor \(P\), that the diagram \(\begin{smallmatrix} P &\subset &M\\ \cup &&\cup\\ K &\subset &N\end{smallmatrix}\) is commuting and co-commuting square (or a non-degenerate commuting square) of type \(\text{II}_1\) factors.