Abstract
In this paper, we study the perturbations of invertible operators and stability of g-frames in Hilbert spaces. In particular, we obtain some conditions under which the perturbations of an invertible operator are still an invertible operator, the perturbations of a right invertible operator or a surjective operator are still a right invertible operator or surjective operator. Then we apply the perturbations of invertible operators to study the stability of g-frames which is close related with the invertibility (or right invertibility) property of operators.
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Guo, X.: g-bases in Hilbert spaces. Abstract and applied analysis, vol. 2012, Article ID 923729, 14 p. doi:10.1155/2012/923729
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This work was partially supported by SWUFE’s Key Subjects Construction Items Funds of 211 Project.
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Guo, X. Perturbations of Invertible Operators and Stability of g-Frames in Hilbert Spaces. Results. Math. 64, 405–421 (2013). https://doi.org/10.1007/s00025-013-0323-9
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DOI: https://doi.org/10.1007/s00025-013-0323-9