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PreprintCC BY 4.0arXiv

New Generalized Dual Banach Frames

  • S. Shahsavand
  • M. Abolghasemi
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Abstract

This paper presents a comprehensive formulation and a systematic investigation of g-dual Banach frames in a Banach space X and its dual space X?. We study the fundamental structural properties of these frames and establish sufficient conditions for their existence. Furthermore, we explore their relationships with other generalized notions of duality in Banach frame theory. Finally, we investigate the stability of g- dual Banach frames under bounded perturbations, demonstrating their robustness and potential applications in functional analysis.

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Cite

BibTeXRIS
BibTeX
@misc{shahsavand2026generalized,
  title = {{New Generalized Dual Banach Frames}},
  author = {S. Shahsavand and M. Abolghasemi},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.28803},
  eprint = {2609.28803},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.28803},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - New Generalized Dual Banach Frames
AU  - S. Shahsavand
AU  - M. Abolghasemi
PY  - 2026
DA  - 2026/09/23
PB  - arXiv
DO  - 10.48550/arxiv.2609.28803
UR  - https://arxiv.org/abs/2609.28803
AB  - This paper presents a comprehensive formulation and a systematic investigation of g-dual Banach frames in a Banach space X and its dual space X?. We study the fundamental structural properties of these frames and establish sufficient conditions for their existence. Furthermore, we explore their relationships with other generalized notions of duality in Banach frame theory. Finally, we investigate the stability of g- dual Banach frames under bounded perturbations, demonstrating their robustness and potential applications in functional analysis.
ER  -