@article{Shen2026, 
author = {Runshuan Shen and Guolin Hou},
title = {A meticulous characterization of the pseudo-residual spectrum and pseudo-continuous spectrum of upper-triangular block operator matrices},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {7},
pages = {20461-20472},
keywords = {pseudospectra, ε-injective, pseudo-residual spectrum, pseudo-continuous spectrum, block operator matrix},
url = {https://www.sciopen.com/article/10.3934/math.2026832},
doi = {10.3934/math.2026832},
abstract = {For    A  ∈      B    (  X  )  ,    B  ∈      B    (  Y  )  ,    C  ∈      B    (  Y  ,  X  )  , let    M  =      (                                        A                                                C                                          0                                                B                                )   denote a    2  ×  2 upper-triangular block operator matrix on    X  ⊕  Y. Employing the spatial decomposition technique and stability of the closed range under small perturbations, this paper investigated the    ε-injectivity and    ε-density of upper-triangular block operator matrices under upper-triangular perturbations. Based on this, we studied meticulous characterization of the pseudo-residual spectrum and pseudo-continuous spectrum of upper-triangular block operator matrices under    2  ×  2 upper-triangular perturbations.}
}