SUMMARY
This discussion centers on the search for examples of Fredholm modules, specifically referencing the difficulty in finding straightforward illustrations. A simple example is provided through a link to PlanetMath, along with additional resources from arXiv and CiteSeerX. The conversation highlights Alain Connes' approach in a French paper, where he divides the Hilbert transform by the imaginary unit 'i' to derive the hermitian involutive F of the Fredholm module, establishing the relationship FF = Id.
PREREQUISITES
- Understanding of Fredholm modules
- Familiarity with hermitian operators
- Knowledge of Hilbert transforms
- Basic comprehension of mathematical papers and notation
NEXT STEPS
- Explore the definition and properties of Fredholm modules in detail
- Study Alain Connes' work on noncommutative geometry
- Investigate the applications of Hilbert transforms in functional analysis
- Review additional examples of Fredholm modules from academic papers
USEFUL FOR
Mathematicians, researchers in functional analysis, and students studying noncommutative geometry will benefit from this discussion, particularly those interested in the practical applications of Fredholm modules.