NORMS FOR COMPACT OPERATORS ON HILBERTIAN OPERATOR SPACES

For Hilbert spaces H, K, a compact operator T: H $\rightarrow$ K, and column, row, operator Hilbert spaces $H_c,\;K_c,\;H_r,\;K_r,\;H_o, K_o$,we show that ${\parallel}T_{co}{\parallel}_{cb}={\parallel}T_{ro}{\parallel}_{cb}={\parallel}T_{oc}{\parallel}_{cb}={\parallel}T_{or}{\parallel}_{cb}={\parallel}T{\parallel}_4$.