Hilbert evolution algebras and its connection with discrete-time Markov chains

Abstract

Evolution algebras are non-associative algebras. In this work we provide an extension of this class of algebras, in the context of Hilbert spaces, capable to deal with infinite-dimensional spaces. We illustrate the applicability of our approach by discussing a connection with discrete-time Markov chains with countable state space.

In this version we correct a mistake in Theorem 3.1 by adding some conditions to obtain a bounded evolution operator. Moreover, we add some examples to illustrate the connection of our results with Markov chains