5 citations · 9 across the 7 of their papers we have counts for
7 papers
Banach-compact operators, -precompactness, and frames in Hilbert -modules
Denis Fufaev, Evgenij Troitsky
For a pair of Hilbert -modules over a -algebra , there are two notions of ``rank-one operators'': $θ_{x,y} : \mathcal{M} \to \math…
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…
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…
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…
Topological and frame properties of certain pathological -algebras
Denis Fufaev
We introduce a classification of locally compact Hausdorff topological spaces with respect to the behavior of -compact subsets, and relying on this classification we study prope…
A Hilbert C*-module with extremal properties
Denis Fufaev
We construct an example of a Hilbert C*-module which shows that Troitsky's theorem on the geometrical essence of A-compact operators between Hilbert C*-modules is not extendable to…
Approximation of linear functionals on the space with convex measure
Denis Fufaev
There are two definitions of the measurable functional on the topological vector space: as a linear and measurable real-valued function and as a pointwise limit of the sequence of…