Quantum law of large numbers for Banach spaces

Abstract

We consider random operators $\Omega \to \mathcal{L}({\ell }_p,{\ell }_p)$ for some $1⩽p<\infty$. 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 $p⩽2$.

11 pages

Cited by in corpus (1)

• The Strong Law of Large Numbers for random semigroups on uniformly smooth Banach spaces