Guardat en:
| Autor principal: | |
|---|---|
| Format: | Preprint |
| Publicat: |
2025
|
| Matèries: | |
| Accés en línia: | https://arxiv.org/abs/2506.01161 |
| Etiquetes: |
Afegir etiqueta
Sense etiquetes, Sigues el primer a etiquetar aquest registre!
|
Taula de continguts:
- In this paper, we introduce the notion of invariant submodule in the theory of Hilbert C*-modules and study some basic properties of bounded adjointable operators and their generalized inverses which have nontrivial invariant submodules. We demonstrate the representation of the solution set of an operator equation on Hilbert C*-modules by taking advantage of invariant submodules. In particular, we consider the special cases of finite dimensional C*-algebras and C*-algebras of compact operators as the underling C*-algebra to simplify our results, and obtain a Lomonosov type theorem for compact operators on some Hilbert C*-modules.