Seminar

Speaker: Marcel Scherer (Saarland University)

Title: The lattice of C*-covers of an operator algebra

Abstract: C*-covers of operator algebras, already studied by Arveson 50 years ago, continue to be a vibrant area of research. Recently, Adam Humeniuk and Christopher Ramsey studied the lattice of C*-covers of operator algebras, focusing on
its structure and whether the lattice can uniquely identify operator algebras up to completely isometric isomorphism.

In my talk, I will characterize the lattices of C*-covers of operator algebras that have only finitely many elements. Interestingly, if the lattice contains more than one element, it must already have uncountably many elements. Additionally, I will present an example of an non-selfadjoint operator algebra with exactly one C*-cover, alongside other related findings.
This is a joint work with Adam Humeniuk and Christopher Ramsey.