James F. Tian

activity

20172026

most citedDual pairs of operators, harmonic analysis of singular non-atomic measures and Krein-Feller diffusion

2 citations · 5 across the 40 of their papers we have counts for

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3 papers · 1 filter

math.OA2026

UCP Extension in Dimension Three

James Tian

We show that every UCP extension problem for a finite dimensional operator system can be reduced to three dimensions after finite matrix amplification. The set of extensions is pre…

math.OA2025

Factorization of positive definite kernels. Correspondences: $C^{*}$ -algebraic and operator valued context vs scalar valued kernels

Palle E. T. Jorgensen, James Tian

We introduce and study a class $M$ of generalized positive definite kernels of the form $K : X \times X \to L (A, L (H))$ , where $A$ is a unital $C^{…

math.OA2024

Operator-Valued Kernels, Machine Learning, and Dynamical Systems

Palle E. T. Jorgensen, James Tian

In the context of kernel optimization, we prove a result that yields new factorizations and realizations. Our initial context is that of general positive operator-valued kernels. W…

UCP Extension in Dimension Three

Factorization of positive definite kernels. Correspondences: C∗-algebraic and operator valued context vs scalar valued kernels

Operator-Valued Kernels, Machine Learning, and Dynamical Systems

Factorization of positive definite kernels. Correspondences: $C^{*}$ -algebraic and operator valued context vs scalar valued kernels