1
$\begingroup$

Can one give an example of two bounded operators A and B in a Hilbert space such that both products AB and BA are of the trace class but their traces are different? If one of them is compact then the traces are equal; if one requires the commutator [A,B] to be of the trace class, not each product separately then the left shift and the right shift give an example.

Improve this question
$\endgroup$
0

1 Answer 1

Reset to default
2
$\begingroup$

See

tr(ab) = tr(ba)?

and

tr(ab)=tr(ba), part 2.

for the Banach space version.

Improve this answer
$\endgroup$

Not the answer you're looking for? Browse other questions tagged .