Gorde:
| Egile Nagusiak: | , |
|---|---|
| Formatua: | Preprint |
| Argitaratua: |
2024
|
| Gaiak: | |
| Sarrera elektronikoa: | https://arxiv.org/abs/2403.01448 |
| Etiketak: |
Etiketa erantsi
Etiketarik gabe, Izan zaitez lehena erregistro honi etiketa jartzen!
|
Aurkibidea:
- In the theory of Hilbert $C^*$-modules over a $C^*$-algebra $A$ (in contrast with the theory of Hilbert spaces) not each bounded operator ($A$-homomorphism) admits an adjoint. The interplay between the sets of adjointable and non-adjointable operators plays a very important role in the theory. We study an intermediate notion of locally adjointable operator $F:M \to N$, i.e. such an operator that $F\circ g$ is adjointable for any adjointable $g: A \to M$. We have introduced this notion recently and it has demonstrated its usefulness in the context of theory of uniform structures on Hilbert $C^*$-modules. In the present paper we obtain an explicit description of locally adjointable operators in important cases.