8 papers
The radial derivative on the graded Möbius algebra
Thomas Sinclair
Let be a simple matroid and let be the graded Möbius algebra of its lattice of flats. The ordered-basis weights of flats define an inner product for which the adjoints o…
Approximate factorization properties for operator systems
Roy Araiza, Larissa Kroell, Travis Russell +1
We show that many of the standard nuclearity properties considered in the literature for the hierarchy of operator system tensor products can be expressed as approximate factorizat…
Finite free convolution via reproducing kernels and squarefree algebras
Thomas Sinclair
We give a structural account of the finite free convolutions of Marcus, Spielman, and Srivastava in terms of reproducing kernel inner products on polynomial spaces and a multilinea…
An operator-theory construction on geometric lattices
Thomas Sinclair
We introduce a canonical operator-theoretic construction associated to a finite geometric lattice, in which a simple nonassociative ``diamond product'' on the lattice basis gives r…
On definability of C*-tensor norms
Isaac Goldbring, Thomas Sinclair
We initiate the study of definability (in the model-theoretic sense) of C*-tensor norms. We show that neither the minimal nor maximal tensor norms are definable uniformly over all…
The model theory of metric lattices: pseudofinite partition lattices
José Contreras Mantilla, Jose Contreras-Mantilla, Thomas Sinclair
We initiate the study of general metric lattices in the context of the model theory of metric structures. As an application we develop a theory of pseudo-finite limits of partition…