Chadi Hamzo, Department of Pure Mathematics, University of Waterloo
"Classification of Finitely Generated Operator Systems"
Borrowing from the theory of representation of commutative C*-algebras by affine maps, we construct a new tool for classifying certain types of finitely generated operator systems. Using this tool, we show that all the information regarding such operator systems is usually encoded in the joint spectra of their generating operators. Furthermore, we compute the C*-envelopes of such operator systems. Using this tool we completely classify operator systems generated by finitely many normal operators. We also settle the classification problem of operator systems generated by a unitary with a spectrum containing 4 points. In addition, we apply this tool to the classification problem of those operator systems generated by a unilateral shift with arbitrary multiplicity or by an isometry and we compute their corresponding C*-envelopes.