Hilbert C*-modules and Morita equivalence

Hilbert C*-modules, adjointable and compact operators, finite projective modules, tensor products, stabilization, Fredholm index, regular operators and continuous fields; completely positive maps, imprimitivity bimodules, induced representations, stable isomorphism and Morita equivalence in K-theory and noncommutative tori.

1. Hilbert C*-modules
2. Adjointable operators
3. Compact operators, multipliers and the strict topology
4. Finite projective modules, frames and \(K_0\)
5. Tensor products and C*-correspondences
6. Kasparov's stabilization theorem
7. Fredholm operators and the K₀ index
8. Unbounded regular operators
9. Continuous fields over locally compact spaces
10. Completely positive maps and the KSGNS construction
11. Imprimitivity bimodules and Morita equivalence
12. The Rieffel correspondence and induced representations (in preparation)
13. Stable isomorphism: the Brown–Green–Rieffel theorem
14. Morita invariance of K-theory and maps induced by correspondences
15. Morita equivalence of noncommutative tori

Original text CC0 1.0 unless the lesson states other terms.