Free biholomorphic functions and operator model theory

Model Theory of Operator Algebras Ii: Model Theory

We introduce a version of logic for metric structures suitable for applications to C*-algebras and tracial von Neumann algebras. We also prove a purely model-theoretic result to the effect that the theory of a separable metric structure is stable if and only if all of its ultrapowers associated with nonprincipal ultrafilters on N are isomorphic even when the Continuum Hypothesis fails.

The proof theory and semantics of operator-free simulation language

Humans can at least apparently conduct deductive reasoning. Various logical inference systems have been developed in order to characterize such human reasoning. The strength of such a properly logical analysis of human reasoning lies in its productivity and predictive power; it enables the theorist to define precisely which data-space the theory covers and then mathematically prove that the the...

Operator Theory and Operator Algebras

Unitarizable representations and fixed points of groups of biholomorphic transformations of operator balls

We show that the open unit ball of the space of operators from a finite dimensional Hilbert space into a separable Hilbert space (we call it “operator ball”) has a restricted form of normal structure if we endow it with a hyperbolic metric (which is an analogue of

Some Extensions of Loewner’s Theory of Monotone Operator Functions

Several extensions of Loewner’s theory of monotone operator functions are given. These include a theorem on boundary interpolation for matrix-valued functions in the generalized Nevanlinna class. The theory of monotone operator functions is generalized from scalarto matrix-valued functions of an operator argument. A notion of κ-monotonicity is introduced and characterized in terms of classical ...