Alessandro De Rango

Alessandro Derango (12 October 1959 – 3 March 2009) was a mathematician who made significant contributions to quantum mechanics, associative algebras, and operator algebras. His PhD dissertation was brought under the supervision of mathematician and physicist Man-Duen Choi, who apparently has only seven students and seven descendants that have worked towards the PhD in this specific field of study.

C*-algebras (pronounced "C-star") are an important area of research in functional analysis, and important tool in the theory of unitary representations of locally compact groups. DeRango’s dissertation abstract, “C*-Algebras Associated with Homomorphisms of the Unit Circle”, made the following proposition:

A complete conjugacy invariant is given for homeomorphisms of the unit circle possessing cyclic points. The irreducible *-representations are given for the C*-algebra that is generated by a universal pair of unitaries (A, B) satisfying BAB* = ℓ(A), where ℓ is a homeomorphism of the unit circle possessing cyclic points. When non-cyclic points are also present, the topological structure of the homeomorphism and its inverse are recovered from the C*-algebra. This is then used to give a complete *-isomorphism invariant for these C*-algebras. It is shown that for any two homeomorphisms with cyclic and non-cyclic points, the corresponding C*-algebras are *-isomorphic if and only if one homeomorphism is topologically equident to the other or its inverse.

DeRango died from a rare cancer in his home in Toronto. Having devoted his career to Mathematics, it was fitting that he died on Square Root Day (03-03-09), an event that happens a few times each century. Despite his repertoire in the sciences, he often expressed his central belief that “Love is eternal.”