Toeplitz Operators on the Bergman Space

Explore the intriguing world of Toeplitz operators on the Bergman space in this 50-minute semi-plenary talk by Nikolai L. Vasilevski from CINVESTAV, Mexico City. Designed for a broad audience, including non-experts in the field, delve into a comprehensive review of results describing algebras generated by Toeplitz operators. Discover surprising findings on the existence of non-isomorphic commutative C∗-algebras and their connection to symbols invariant under maximal Abelian subgroups of unit ball biholomorphisms. Investigate the unexpected emergence of Banach algebras, often non-semisimple, and explore the challenges in identifying compact sets of maximal ideals and describing their radicals. Examine non-commutative C∗-algebras generated by Toeplitz operators with symbols invariant under subgroup actions, and uncover how different types of actions lead to vastly different algebraic properties. Gain valuable insights into this complex mathematical topic through Vasilevski's expert presentation at the Schmid College, Chapman University.