Spectral enclosures for some unbounded \(n\times n\) operator matrices

In this paper, we establish the enclosures for the spectrum of unbounded \(n\times n\) $n\times n$ operator matrices in a Banach space. For diagonally dominant and off-diagonally dominant operator matrices, we present a new Gershgorin-type results on the localization of the spectrum by using the Schur complements and the quadratic complements, respectively, that no longer requires dominance order of 0 nor \(<1\) $<1$ .