Quantum Law of Large Numbers for Banach Spaces

We consider random operators \(\Omega\to\mathcal{L}(\ell_{p},\ell_{p})\) for some \(1\leqslant p<\infty\) . The law of large numbers is known in the case \(p=2\) in the form of usual law of large numbers. Instead of sum of i.i.d. variables there may be considered the composition of random semigroups \(e^{A_{i}t/n}\) . We obtain the law of large numbers for the case \(p\leqslant 2\) .