Module-valued ordinary differential equations and structure of solution spaces

Shengda Liu; Yu-Zhe Liu; Keyu Tao

Module-valued ordinary differential equations and structure of solution spaces

Functional Analysis 2026-05-12 v2 Category Theory

Authors: Shengda Liu , Yu-Zhe Liu , Keyu Tao

Abstract

We define and study ordinary differential equations (ODEs) for functions valued in a Banach module $V$ over a finite-dimensional $\Bbbk$ -algebra $\mathit{\Lambda}$ by using the tensor of Banach modules. Furthermore, we show that the solution space of a homogeneous linear ODE as above is shown to be a finitely generated $\mathit{\Lambda}$ -submodule.

Keywords

ordinary differential equations banach spaces banach algebras

Cite

@article{arxiv.2605.00097,
  title  = {Module-valued ordinary differential equations and structure of solution spaces},
  author = {Shengda Liu and Yu-Zhe Liu and Keyu Tao},
  journal= {arXiv preprint arXiv:2605.00097},
  year   = {2026}
}

Comments

37pages. We have corrected the erroneously used left module structure and, using the projective tensor product norm, corrected the norm of an important left module

Module-valued ordinary differential equations and structure of solution spaces

Abstract

Keywords

Cite

Comments

Related papers