The Strong Law of Large Numbers for random semigroups with unbounded generators on uniformly smooth Banach spaces

Fuente: arXiv
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Main Authors: Dzhenzher, S. V., Sakbaev, V. Zh.
Format: Preprint
Published: 2026
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author Dzhenzher, S. V.
Sakbaev, V. Zh.
author_facet Dzhenzher, S. V.
Sakbaev, V. Zh.
contents We consider random linear unbounded operators on a Banach space $\mathcal{X}$. For example, such random operators may be random quantum channels. The Law of Large Numbers is known when $\mathcal{X}$ is a Hilbert space, in the form of the usual Law of Large Numbers for random operators, and in some other particular cases. Instead of the sum of i.i.d. variables, there may be considered the composition of random semigroups $e^{A_i t/n}$. We obtain the Strong Law of Large Numbers in Strong Operator Topology for random semigroups of unbounded linear operators on a uniformly smooth Banach space.
format Preprint
id arxiv_https___arxiv_org_abs_2601_04612
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle The Strong Law of Large Numbers for random semigroups with unbounded generators on uniformly smooth Banach spaces
Dzhenzher, S. V.
Sakbaev, V. Zh.
Functional Analysis
Probability
We consider random linear unbounded operators on a Banach space $\mathcal{X}$. For example, such random operators may be random quantum channels. The Law of Large Numbers is known when $\mathcal{X}$ is a Hilbert space, in the form of the usual Law of Large Numbers for random operators, and in some other particular cases. Instead of the sum of i.i.d. variables, there may be considered the composition of random semigroups $e^{A_i t/n}$. We obtain the Strong Law of Large Numbers in Strong Operator Topology for random semigroups of unbounded linear operators on a uniformly smooth Banach space.
title The Strong Law of Large Numbers for random semigroups with unbounded generators on uniformly smooth Banach spaces
topic Functional Analysis
Probability
url https://arxiv.org/abs/2601.04612