Multipliers of elementary operators and comparison of row and column space Schatten \(p\) norms (Q734918)

Let \(H\) be a separable infinite-dimensional complex Hilbert space. For a symmetric gauge function \(\Phi\), let \(C_\Phi(H)\) be the associated ideal in \(B(H)\). In the paper under review, some estimates for the norm of weighted elementary operators \(\sum_{n=1}^{\infty} C_n Z_n A_n \otimes B_n W_n D_n:~C_\Phi(H) \to C_{\Phi'}(H)\) are given. In particular, the norm of \(\sum_{n=1}^{\infty} C_n Z_n A_n \otimes A_{n}^{*} W_n C_{n}^{*}\) is related to the norms of \(\sum_{n=1}^{\infty}A_n \otimes A_{n}^{*}\) and \(\sum_{n=1}^{\infty}C_n \otimes C_{n}^{*}\).