Michael Hartz, Stefan Richter and I recently uploaded our paper von Neumann’s inequality for row contractive matrix tuples to the arxiv.
The main result is the following.
We prove that for all , there exists a constant such that for every row contraction consisting of commuting matrices and every polynomial , the following inequality holds:
We then apply this result and the considerations involved in the proof to several open problems from the literature. I won’t go into that because I think that the abstract and introduction do a good job of explaining what we do in the paper. In this post I will write about how this collaboration with Michael and Stefan started, and give some heuristic explanation why our result is not trivial.Read the rest of this entry »