13 citations · 61 across the 20 of their papers we have counts for
8 papers · 1 filter
Vector spaces with an order unit
Vern Paulsen, Mark Tomforde
We develop a theory of ordered *-vector spaces with an order unit. We prove fundamental results concerning positive linear functionals and states, and we show that the order (semi)…
Computing Stabilized Norms for Quantum Operations via the Theory of Completely Bounded Maps
Nathaniel Johnston, David W. Kribs, Vern I. Paulsen
The diamond and completely bounded norms for linear maps play an increasingly important role in quantum information science, providing fundamental stabilized distance measures for…
A Constrained Nevanlinna-Pick Interpolation Problem
Kenneth R. Davidson, Vern I. Paulsen, Mrinal Raghupathi +1
We obtain necessary and sufficient conditions for Nevanlinna-Pick interpolation on the unit disk with the additional restriction that all analytic interpolating functions satisfy $…
Injectivity and Projectivity in Analysis and Topology
Don Hadwin, Vern I. Paulsen
We give new proofs for many injectivity results in analysis that make more careful use of the duality between unital abelian C*-algebras and compact Hausdorff spaces. We then exten…
Some new equivalences of Anderson's paving conjectures
Vern I. Paulsen, Mrinal Raghupathi
Anderson's paving conjectures are known to be equivalent to the Kadison-Singer problem. We prove some new equivalences of Anderson's conjectures that require the paving of smaller…
A Dynamical Systems Approach to the Kadison-Singer Problem
Vern I. Paulsen
In these notes we develop a link between the Kadison-Singer problem and questions about certain dynamical systems. We conjecture that whether or not a given state has a unique exte…