Computational Models for <i>(M, K)</i>-Quasi-*-Parahyponormal Operators

We study the two-parameter class of <i>(M, k)</i>-Quasi-∗-Parahyponormal operators on separable Hilbert spaces, which strictly enlarges the traditional parahyponormal and paranormal hierarchies. Analytically we prove three fundamental results: Every operator in the class has finite ascent and enjoys the single-valued extension property (SVEP); The Browder–Weyl partition holds, so Weyl’s theorem is valid; A non-trivial closed invariant subspace exists whenever the commutant contains a non-zero compact element. Complementing these theorems, we introduce a proposed computational framework that realises the abstract operators as large weighted-shift matrices, verifies the defining quadratic inequality, and computes eigenvalues as well aaccelerated pseudospectra. Together, the analytic results and the computational framework deepen the spectral theory of <i>(M, k)</i>-Quasi-∗-Parahyponormal Operators and supply the first large-scale numerical evidence for their structural properties.