Matrix Problems in Hilbert Spaces

TL;DR

This paper investigates matrix classification problems in Hilbert spaces, focusing on orthoscalar representations of quivers and posets, and provides a criterion to determine when these problems are manageable.

Contribution

It introduces a criterion for the tameness of classifying indecomposable orthoscalar quiver representations in Hilbert spaces.

Findings

Established a criterion for tameness in classification problems.

Characterized orthoscalar representations of quivers and posets.

Provided insights into the complexity of matrix problems in infinite-dimensional settings.

Abstract

We consider matrix problems in Hilbert spaces (orthoscalar representations of quivers and posets). A criterion of tameness of the problem of classification of indecomposable orthoscalar representations of a quiver is given.