Complex Bounded Operators

José Manuel Rodríguez Caballero 🌐 and Dominique Unruh 🌐

September 18, 2021

This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.


We present a formalization of bounded operators on complex vector spaces. 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.
BSD License


Theories of Complex_Bounded_Operators