Complex Bounded Operators in Isabelle/HOL

arXiv (Cornell University)

Abstract

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.

Authors 2

1. Dominique Unruh Aachen

   RWTH Aachen University · University of Tartu

   Affiliation as printed

   RWTH Aachen, Germany

   University of Tartu, Estonia

2. José Manuel Rodríguez Caballero

   Université Laval

   Affiliation as printed

   Mathématiques et statistique - Faculté des sciences et de génie - Université Laval, Québec, Canada