2026-08-26T00:57:22Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:26977 2026-07-16T09:49:33Z ddc:004 open_access

Complex Bounded Operators in Isabelle/HOL Unruh, Dominique Caballero, José Manuel Rodríguez Formalized mathematics functional analysis bounded operators We present a formalization of bounded operators on complex vector spaces in Isabelle/HOL. Our formalization contains material on complex vector spaces (normed spaces, Banach spaces, Hilbert spaces) that complements and goes beyond the developments of real vectors spaces in the Isabelle/HOL standard library. We define the type of bounded operators between complex vector spaces (cblinfun) and develop the theory of unitaries, projectors, extension of bounded linear functions (BLT theorem), adjoints, Loewner order, closed subspaces and more. For the finite-dimensional case, we provide code generation support by identifying finite-dimensional operators with matrices as formalized in the Jordan_Normal_Form AFP entry. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Dominique Unruh and José Manuel Rodríguez Caballero 2026 Is Part Of LIPIcs, Volume 382, 17th International Conference on Interactive Theorem Proving (ITP 2026) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ITP.2026.3 urn:nbn:de:0030-drops-269772 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2026.3 eng https://creativecommons.org/licenses/by/4.0/legalcode