On Hilbert bases of cuts

On duality of modular G-Riesz bases and G-Riesz bases in Hilbert C*-modules

In this paper, we investigate duality of modular g-Riesz bases and g-Riesz bases in Hilbert C*-modules. First we give some characterization of g-Riesz bases in Hilbert C*-modules, by using properties of operator theory. Next, we characterize the duals of a given g-Riesz basis in Hilbert C*-module. In addition, we obtain sufficient and necessary condition for a dual of a g-Riesz basis to be agai...

Operator-valued bases on Hilbert spaces

In this paper we develop a natural generalization of Schauder basis theory, we term operator-valued basis or simply ov-basis theory, using operator-algebraic methods. We prove several results for ov-basis concerning duality, orthogonality, biorthogonality and minimality. We prove that the operators of a dual ov-basis are continuous. We also dene the concepts of Bessel, Hilbert ov-basis and obta...

New characterizations of fusion bases and Riesz fusion bases in Hilbert spaces

In this paper we investigate a new notion of bases in Hilbert spaces and similar to fusion frame theory we introduce fusion bases theory in Hilbert spaces. We also introduce a new denition of fusion dual sequence associated with a fusion basis and show that the operators of a fusion dual sequence are continuous projections. Next we dene the fusion biorthogonal sequence, Bessel fusion basis, Hil...

Hilbert Bases of Cuts Hilbert Bases of Cuts

Let X be a set of vectors in R m. X is said to be a Hilbert base if every vector in R m which can be written both as a linear combination of members of X with nonnegative coeecients and as a linear combination with integer coeecients can also be written as a linear combination with nonnegative integer coeecients. Denote by H the collection of the graphs whose family of cuts is a Hilbert base. I...

Generalized Frames in Hilbert Spaces