Model Theory of a Hilbert Space Expanded with an Unbounded Closed Selfadjoint Operator

2011/02/11 by Camilo Argoty, Argoty, Camilo
Mathematics · #Advanced Operator Algebra Research #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics #math.LO #math.SP #msc:03C45 #msc:03C48 #msc:03C52 #msc:03C65 #msc:03C98 #msc:28E15 #msc:37K05 #msc:46C05 #msc:46C07 #msc:47A05

paper · pdf · doi:10.48550/arxiv.1102.2454

arxiv created 2011/06/06 · arxiv updated 2011/06/07

Abstract

We study a closed unbounded self-adoint operator Q acting on a Hilbert space H in the framework of Metric Abstract Elementary Classes (MAECS). We build a suitable MAEC for (H,Q), prove it is aleph 0 stable up to perturbations and characterize non-splitting and show it has the same properties as non-forking in superstable first order theorues. Also, we characterize equality, orthogonality and domination of (Galois) types in that MAEC.

Related

• Model theory of Hilbert spaces expanded by normal operators
• On a class of Model Hilbert Spaces
• On some extensions of the A-model
• Notes on the Krupa-Zawisza Ultrapower of Self-Adjoint Operators
• Unbounded operators in Hilbert space, duality rules, characteristic projections, and their applications