Robert Schatten (born 1935) is a German‑American mathematician notable for his contributions to functional analysis, particularly the theory of operator ideals and Schatten class operators. He earned his Ph.D. from the University of Göttingen in 1960 under the supervision of Wilhelm Klingenberg, with a dissertation on spectral theory.
Schatten held academic positions at several institutions, including the University of California, Berkeley, and the University of Colorado Boulder, where he served as a professor of mathematics. His research focused on the properties of compact operators on Hilbert spaces, leading to the introduction of the Schatten p‑norms (also called Schatten norms) for p ≥ 1. These norms define a family of ideals in the algebra of bounded linear operators, now commonly referred to as Schatten classes $ \mathcal{C}_p $. The classification of operators according to these norms has become a standard tool in functional analysis, quantum mechanics, and related fields.
Among his published works are:
- “Norm Ideals of Completely Continuous Operators” (1960), a monograph that systematically presented the theory of Schatten classes.
- Numerous articles on operator theory in journals such as Transactions of the American Mathematical Society and Journal of Functional Analysis.
Schatten's contributions have been recognized by his election to the American Mathematical Society and by the naming of the “Schatten norm” and “Schatten class” concepts that bear his name in mathematical literature. He retired from active teaching in the early 2000s but remains cited in contemporary research on operator algebras.
