Krein空间中对偶框架的稳定性OA

The theory and methods of Krein space operators have garnered significant attention due to their important applications in mathematics and engineering.In recent years,the concept of frames has been introduced into Krein spaces.As a generalization of frames,dual frames provide multiple representations for signals,thereby offering more choices and flexibility in signal processing.However,the indefiniteness of the inner product in Krein spaces leads to fundamental differences between its frame theory and that of Hilbert spaces,making classical perturbation stability theories not directly applicable.By employing frame operators and the Minkowski inequality,the stability of dual frames in Krein spaces under perturbations from sequences and Bessel sequences is investigated,and corresponding proofs are provided.