13 papers
Intrinsic Geometry of Categorified Spectral Objects
Shih-Yu Chang
This paper develops the intrinsic geometry of the categorified spectral object associated with an admissible operator-semantic system in the Categorified S…
Operator Inequalities in -Product Tensor Algebras: Invariance and Transform Sensitivity
Shih-Yu Chang, Michael K. Ng
We study classical operator inequalities in -product tensor algebras (a transformation -based generalization of the -product framework) for third-order tensors. Although…
Categorified Spectral Duality: From Operator Systems to Spectral Stacks and Back
Shih-Yu Chang
Classical Gelfand duality provides an equivalence between commutative C-star algebras and topological spaces, but fails to furnish a geometric object for noncommutative operator sy…
A Universal Theory of Spectral Propagation for Compositional Operator Networks
Shih-Yu Chang
Classical spectral theory lacks a framework for understanding how spectra propagate through compositional systems like deep neural networks, feedback control loops, and quantum cir…
Interaction Residues and Localized Spectral Defects in Stratified Operadic Systems
Shih-Yu Chang
We develop a framework for studying how global spectral structure emerges from interacting local sectors in stratified operadic systems. The central object is the interaction resid…
Spectral Operadic Calculus: Norm-Analytic Functor Calculus
Shih-Yu Chang
Classical spectral theory provides powerful tools for analyzing linear operators, but does not extend naturally to nonlinear or compositional settings. In particular, there is no g…