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PreprintarXiv licencearXiv

Generalized [v,w]-core inverse in Banach *-algebras

  • Huanyin Chen
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Abstract

We introduce the generalized weighted core inverse with respect to two elements in a Banach *-algebra, extending the framework of existing generalized inverses. This new generalized inverse is characterized via the generalized weighted core decomposition, and its representations are established using the weighted g-Drazin inverse. We investigate the polar-like and principal ideal properties to reveal its structural behavior. Consequently, applications to complex matrices are derived. This finds encompasses both the core-EP and generalized core inverses, significantly broadening the theoretical framework.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026generalized,
  title = {{Generalized [v,w]-core inverse in Banach *-algebras}},
  author = {Huanyin Chen},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.06866},
  eprint = {2610.06866},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.06866},
}
RIS
TY  - UNPB
TI  - Generalized [v,w]-core inverse in Banach *-algebras
AU  - Huanyin Chen
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.06866
UR  - https://arxiv.org/abs/2610.06866
AB  - We introduce the generalized weighted core inverse with respect to two elements in a Banach *-algebra, extending the framework of existing generalized inverses. This new generalized inverse is characterized via the generalized weighted core decomposition, and its representations are established using the weighted g-Drazin inverse. We investigate the polar-like and principal ideal properties to reveal its structural behavior. Consequently, applications to complex matrices are derived. This finds encompasses both the core-EP and generalized core inverses, significantly broadening the theoretical framework.
ER  -