Nuclear operators and the Grothendieck-Lidskii formula in quaternionic space

In this talk we discuss the Grothendieck-Lidskii formula in quaternionic Hilbert spaces, along with the particularities of the problem, which include, among others, the definition of an appropriate trace that differs from the usual one.
We will also briefly discuss r-nuclear operators in quaternionic Banach (or, more generally, locally convex) spaces X and the associated Grothendieck-Lidskii's formula for the case r greater or equal 2/3. In order to establish these results, the use of the aforementioned traces (and their invariance with respect to the basis choices) is essential.
To conclude, we briefly discuss how the (seemingly ad hoc) introduced trace actually arise as the canonical form in tensor products of quaternionic vector spaces. This is a joint work with P. Cerejeiras, F. Colombo, U. Kähler, and I. Sabadini.