Upper triangular matrices property on unbounded Hilbert spaces: Different Weyl Type findings

The usage of unbounded Hilbert spaces, in particular the Hilbert spaces of analytically functions, is emerging in applications. Many areas of mathematics and physics, including quantum physics and control theory, have applications for them. In this attempt, we recommend these space types and a self-adjoint extension choice. The analysis of the unbounded upper triangular operator matrix with diagonal domain is one of the key characteristics of such spaces. The essential spectrum, the Weyl spectrum, and the Browder spectrum of this operator matrix must coincide with the union of the essential spectrum, the Weyl spectrum, and the Browder spectra of the diagonal entries in order for this to happen.