Triviality of a trace on the space of commuting trace-class self-adjoint operators
arXiv:0803.2471
Abstract
In the present article, we investigate a possibility of a real-valued map on the space of tuples of commuting trace-class self-adjoint operators, which behaves like the usual trace map on the space of trace-class linear operators. It turns out that such maps are related with continuous group homomorphisms from the Milnor's -group of the real numbers into the additive group of real numbers. Using this connection, it is shown that any such trace map must be trivial.
5 pages