Let X and Y be Hilbert C *-modules over a C *-algebra, and ϕ : X × Y → [0, ∞) be a function. A (not necessarily linear) mapping f : X → Y is called a ϕ-perturbed adjointable mapping if there exists a (not necessarily linear) mapping g : Y → X such that In this paper, we investigate the stability of adjointable mappings on Hilbert C *-modules and discuss the case where the modules are self-dual....

A notion of curvature is introduced in multivariable operator theory, that is, for commuting d tuples of operators acting on a common Hilbert space whose “rank” is finite in an appropriate sense. The curvature invariant is a real number in the interval [0, r] where r is the rank, and for good reason it is desireable to know its value. For example, there are significant and concrete consequences...