Which operators are the self-commutators of compact operators?
Which operators are the self-commutators of compact operators?
It is shown that, for a hermitian operator <italic>T</italic> on a Hubert space <italic>H</italic>, the following three statements are equivalent: (i) <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper T equals upper A Superscript asterisk Baseline upper A minus upper A upper A Superscript asterisk"> <mml:semantics> <mml:mrow> <mml:mi>T</mml:mi> <mml:mo>=</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>A</mml:mi> …