# Nest algebras in an arbitrary vector space

## TL;DR

This paper explores the properties of nest algebras within arbitrary vector spaces, extending the understanding beyond the classical Hilbert space setting and analyzing their invariant subspace structures.

## Contribution

It introduces a general framework for nest algebras in arbitrary vector spaces, broadening the scope beyond Hilbert space operators.

## Key findings

- Characterization of nest algebras in arbitrary vector spaces
- Comparison with bounded operator algebras on Hilbert spaces
- Insights into invariant subspace structures

## Abstract

We examine the properties of algebras of linear transformations that leave invariant all subspaces in a totally ordered lattice of subspaces of an arbitrary vector space. We compare our results with those that apply for the corresponding algebras of bounded operators that act on a Hilbert space.