Year: 2025
Type: article
Abstract: We extend our previous definition of K-theoretic invariants for operator systems based on hermitian forms to higher K-theoretical invariants. We realize the need for a positive parameter δ \delta as a measure for the spectral gap of the representatives for the K-theory classes. For each δ \delta and integer p ≥ 0 p \geq 0 this gives operator system invariants V p δ ( − , n ) \mathcal {V}_p^\delta (-,n) , indexed by the corresponding matrix size. The corresponding direct system of these invariants has a direct limit that possesses a semigroup structure, and we define the K p δ K_p^\delta -groups as the corresponding Grothendieck groups. This is an invariant of unital operator systems, and, more generally, an invariant up to Morita equivalence of operator systems. Moreover, there is a formal periodicity that reduces all these groups to either K 0 δ K_0^\delta or K 1 δ K_1^\delta . We illustrate our invariants by means of the spectral localizer.
DOI: 10.1090/tran/9601
Author: Walter van Suijlekom
Institution: Radboud University Nijmegen
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4417046732