LAUSR

In this paper, we define the g-Riesz-dual of a given special operator-valued sequence with respect to g-orthonormal bases for a separable Hilbert space. We demonstrate that the g-R-dual keeps some synchronous frame properties with the operator-valued sequence given. We also display some Schauder basis-like properties of the g-R-dual in the light of the properties of the given sequence. In particular, the g-R-dual can be characterized by the use of another sequence, related to the given sequence. Finally, a special sequence is constructed to build the relationship between an operator-valued sequence and a g-Riesz sequence.