3 papers
math.OA2025
Locally unital -algebras do not admit frames
Denis Fufaev
We study nonunital -algebras such that for any element there exists a local unit and prove that in such algebras there are no frames. This fact was previously known only for c…
math.OA2024
Locally adjointable operators on Hilbert -modules
Denis Fufaev, Evgenij Troitsky
In the theory of Hilbert -modules over a -algebra (in contrast with the theory of Hilbert spaces) not each bounded operator (-homomorphism) admits an adjoint. The…
math.OA2024
A new uniform structure for Hilbert -modules
Denis Fufaev, Evgenij Troitsky
We introduce and study some new uniform structures for Hilbert -modules over an algebra . In particular, we prove that in some cases they have the same totally bounded sets…