Complex Bounded Operators in Isabelle/HOL
By: Dominique Unruh, José Manuel Rodríguez Caballero
Functional analysis, especially the theory of Hilbert spaces and of operators on these, form an important area in mathematics. We formalized the Isabelle/HOL library Complex_Bounded_Operators containing a large amount of theorems about complex Hilbert spaces and (bounded) operators on these. Specifically, we formalize the properties complex vector spaces, inner product (and Hilbert) spaces, one-dimensional spaces, bounded operators, adjoints, unitaries, projections, extensions of bounded operators (BLT-theorem), positive operators, square-summable sequences and much more. Additionally, we provide support for code generation in the finite-dimensional case.
Similar Papers
Transfinite Iteration of Operator Transforms and Spectral Projections in Hilbert and Banach Spaces
Functional Analysis
Makes math problems solve themselves faster.
L-Mosaics and Bounded Join-Semilattices in Isabelle/HOL
Logic in Computer Science
AI helps prove math ideas about quantum logic.
Higher order differential calculus in mathlib
Logic in Computer Science
Makes math proofs easier for computers to check.