Stability and Duality of Operator-Valued Frames under Perturbations

Ponente(s): Slavisa Djordjevic .

This talk presents recent advances on the stability and duality properties of operator-valued (OPV) frames under various perturbations. OPV-frames are shown to be robust, maintaining their structure under operator-based disturbances, especially when a significant size gap exists between frames. Closeness between the analysis operators of two OPV-frames is proven to ensure the formation of a valid OPV-frame, reflecting their continuity and resilience. On the duality side, an alternative characterization of OPV-frame duals via families of Bessel OPV-frames is introduced, and the uniqueness of duals for Riesz OPV-frames is established. These results provide a strengthened theoretical foundation for stable and reliable frame-based representations in applications such as signal processing, functional analysis, and operator theory.