Positive self-commutators of positive operatorsDrnovšek, Roman (Avtor) Kandić, Marko (Avtor) Banach latticespositive operatorscommutatorsWe consider a positive operator $A$ on a Hilbert lattice such that its self-commutator $C = A^* A - A A^*$ is positive. If $A$ is also idempotent, then it is an orthogonal projection, and so $C = 0$. Similarly, if $A$ is power compact, then $C = 0$ as well. We prove that every positive compact central operator on a separable infinite-dimensional Hilbert lattice ${\mathcal H}$ is a self-commutator of a positive operator. We also show that every positive central operator on ${\mathcal H}$ is a sum of two positive self-commutators of positive operators.20252025-10-20 13:52:31Članek v reviji175179sl