Semigroups of finite-dimensional random projections

TL;DR

This paper provides a comprehensive description of stochastic semigroups of finite-dimensional projections in Hilbert space, focusing on their geometric properties and the asymptotic behavior of widths of compact sets.

Contribution

It offers a complete characterization of the geometry of these semigroups based on the asymptotic analysis of widths of compact subsets.

Findings

Characterization of the geometry of stochastic semigroups of projections

Analysis of asymptotic behavior of widths of compact sets

Complete description of the structure of finite-dimensional projection semigroups

Abstract

In this paper we present a complete description of a stochastic semigroup of finite-dimensional projections in Hilbert space. The geometry of such semigroups is characterized by the asymptotic behavior of the widths of compact subsets with respect to the subspaces generated by the semigroup operators.