Triviality of a trace on the space of commuting trace-class self-adjoint operators

Details Triviality of a trace on the space of commuting trace-class self-adjoint operators Triviality of a trace on the space of commuting trace-class self-adjoint operators

2008-03-17

arxiv.org/abs/0803.2471v2

Mathematics

Operator Algebras

5 pages

Scientific paper

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 $K$-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.

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