Analytic foundations for Kasparov's KK-theory

These independently written proof readings provide the stated bounded-operator, Banach, spectral and cyclic foundations.

• Bounded trace ideals and rectangular cyclicity
• Compact spectral decomposition and Schatten estimates
• Baire, Banach estimates and bounded inverses
• Positive spectral measures and original operator domains
• Cyclic cohomology and its algebraic foundations

For first-order differential domains on a closed manifold, see Lesson 03, Corollary 4.2. Regular Hilbert-module bounded transforms are proved in Lesson 11. The relative classical-symbol KK class is treated in Lesson 15, Section 7. Lesson 04, Section 7 proves the bounded Fredholm-character comparison.

Programme source and component record.