Quantitative Stability of Invertible Hilbert-Schmidt Frame Multipliers

Hilbert-Schmidt (HS) frames provide an operator-valued extension of classical frames with coefficients in the Hilbert space C۲, and their associated multipliers generalize frame operators in applications ranging from time-frequency analysis to numerical operator approximation. We study invertible HS-frame multipliers and establish quantitative stability under perturbations of both the symbol and the generating HS-frame data. Specifically, we give an explicit margin on symbol perturbations ensuring persistence of invertibility, together with a norm-convergent Neumann-series inverse formula and a Lipschitz-type bound for the perturbed inverse. We also derive an operator-norm tolerance for perturbations of the underlying HS-frames measured via synthesis-operator deviations.

کلیدواژه ها:

Hilbert-Schmidt frame ، HS-Riesz basis ، frame multiplier ، invertibility ، perturbation ، Neumann series