6 papers
-extreme maps and -homomorphisms from to finite von Neumann algebras
Dimitrios Giannakis, Michael Montgomery, Travis Russell
Given a unital inclusion of -algebras and a unital inclusion into a von Neumann algebra , we invest…
Measure-free Koopman-von Neumann dynamics and noncommutative Geometry
Dimitrios Giannakis, Michael Montgomery
The Koopman-von Neumann formulation of classical statistical dynamics maps the isometric evolution of probability densities in under the Liouville equation to a unitary evolu…
On Algebras of Functions over Infinite Dimensions
Dimitrios Giannakis, Mohammad Javad Latifi Jebelli, Michael Montgomery
We introduce a family of reproducing kernel Hilbert spaces of holomorphic functions defined on an infinite--dimensional domain in a separable Hilbert space, $\mathbb…
Koopman and transfer operator techniques from the perspective of quantum theory
Dimitrios Giannakis, Michael Montgomery
The study of mathematical connections between operator-theoretic formulations of classical dynamics and quantum mechanics began at least as early as the 1930s in work of Koopman an…
Tensor network approximation of Koopman operators
Dimitrios Giannakis, Mohammad Javad Latifi Jebelli, Michael Montgomery +3
We propose a tensor network framework for approximating the evolution of observables of measure-preserving ergodic systems. Our approach is based on a spectrally-convergent approxi…
An algebra structure for reproducing kernel Hilbert spaces
Dimitrios Giannakis, Michael Montgomery
Reproducing kernel Hilbert spaces (RKHSs) are Hilbert spaces of functions where pointwise evaluation is continuous. There are known examples of RKHSs that are Banach algebras under…