Ergodic theorems for flows in the ideals of compact operators

Let $\mathcal H$~--- be an infinite-dimensional complex Hilbert space, let $(\mathcal B(\mathcal H), \|\cdot\|_\infty)$~--- $C^\star$ - algebra of all bounded linear operators acting in $\mathcal H$, and let \ $\mathcal C_E$ \ l be the symmetric
ideal of compact operators in $\mathcal H$, generated by the fully symmetric sequence space \ $E\subset c_0$.If $T_t:\mathcal B(\mathcal H)\to\mathcal B(\mathcal H),\ t\geq 0$, is a semigroup of positive Dunford-Schwartz operators, which is strongly continuous on $C_{1}$, then the following versions of individual and mean ergodic theorems $x\in \mathcal C_E$ the net $A_t(x)=\frac1t\int_0^tT_s(x)ds$ converges to some \ $\widehat{x} \in \mathcal C_E $ with respect to the norm \ $\|\cdot\|_\infty$ \ при \ $t\to \infty$; \ moreover, if $E$ is separable and $E\neq l_1$ (as a set), then \ $\lim\limits_{t \to \infty}\|A_t (x)-\widehat{x}\|_{\mathcal C_E} = 0$.