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Browder spectra of closed upper triangular operator matrices

  • Received: 10 September 2023 Revised: 16 January 2024 Accepted: 18 January 2024 Published: 25 January 2024
  • MSC : 47A25, 47A55

  • Let $ T_{B} = \left[\begin{array}{ll} A & B \\ 0 & D \end{array}\right] $ be an unbounded upper operator matrix with diagonal domain, acting in $ \mathcal H \oplus\mathcal K $, where $ \mathcal H $ and $ \mathcal K $ are Hilbert spaces. In this paper, some sufficient and necessary conditions are characterized under which $ T_{B} $ is Browder (resp., invertible) for some closable operator $ B $ with $ \mathcal D(B)\supset \mathcal D(D) $. Further, a sufficient and necessary condition is given under which the Browder spectrum (resp., spectrum) of $ T_{B} $ coincides with the union of the Browder spectrum (resp., spectrum) of its diagonal entries.

    Citation: Qingmei Bai, Alatancang Chen, Jingying Gao. Browder spectra of closed upper triangular operator matrices[J]. AIMS Mathematics, 2024, 9(2): 5110-5121. doi: 10.3934/math.2024248

    Related Papers:

  • Let $ T_{B} = \left[\begin{array}{ll} A & B \\ 0 & D \end{array}\right] $ be an unbounded upper operator matrix with diagonal domain, acting in $ \mathcal H \oplus\mathcal K $, where $ \mathcal H $ and $ \mathcal K $ are Hilbert spaces. In this paper, some sufficient and necessary conditions are characterized under which $ T_{B} $ is Browder (resp., invertible) for some closable operator $ B $ with $ \mathcal D(B)\supset \mathcal D(D) $. Further, a sufficient and necessary condition is given under which the Browder spectrum (resp., spectrum) of $ T_{B} $ coincides with the union of the Browder spectrum (resp., spectrum) of its diagonal entries.



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