The spectrum of operator extensions to free Banach Lattices

What the math gives to ML

The paper provides a constructive spectral-functional-calculus mechanism: extending a linear operator to a free Banach lattice creates new eigenvalues whose phases are finite products of phases already present in the original operator. The transferable asset is not the abstract spectrum characterization itself, but the ability to generate nonlinear, positively homogeneous interaction features with predictable scaling under a linear transformation. A practical neural-network adaptation is a spectral feature lift for complex-valued or paired-real hidden states, where fractional homogeneous products of approximately identified eigenmodes are appended as channels and tested for improved long-horizon stability or expressivity.