DUAL BASES FUNCTIONS IN SUBSPACES

Riesz Bases in Subspaces of L 2 (ir + ) Riesz Bases in Subspaces of L 2 (ir + )

In recent investigation 8] concerning the asymptotic behavior of Gram Schmidt or-thonormalization procedure applied to the nonnegative integer shifts of a given function, the problem of determining whether or not such functions form a Riesz system in L 2 (IR +) arose. In this note, we provide a suucient condition to determine whether the nonnegative translates form a Riesz system on L 2 (IR +)....

Bipartite subspaces having no LOCC-distinguishable bases

It is proved that there exist subspaces of bipartite tensor product spaces that have no orthonormal bases that can be perfectly distinguished by means of LOCC protocols. A corollary of this fact is that there exist quantum channels having sub-optimal classical capacity even when the receiver may communicate classically with a third party that represents the channel’s environment.

Extending Functions in the Model Subspaces of H^2(R) to C

Positive Bases in Ordered Subspaces with the Riesz Decomposition Property

In this article we suppose that E is an ordered Banach space the positive cone of which is defined by a countable familyF={fi|i ∈ N} of positive continuous linear functionals of E, i.e. E+ = {x ∈ E | fi(x) ≥ 0, for each i} and we study the existence of positive (Schauder) bases in the ordered subspaces X of E with the Riesz decomposition property. So we consider the elements x of E as sequences...

Smooth Functions in Star-invariant Subspaces

In this note we summarize some necessary and sufficient conditions for subspaces invariant with respect to the backward shift to contain smooth functions. We also discuss smoothness of moduli of functions in such subspaces.