Intertwining, analytic structure, and the trace norm estimate -- Toeplitz operators on odd spheres -- Invariant subspaces of non-quasitriangular operators -- Unitary equivalence modulo the compact operators and extensions of C*-algebras -- Ext(X) from a homological point of view -- Integral operators: Traces, index, and homology -- The determinant invariant for operators with trace class self commutators