Marko Kandić

From local to global ideal-triangularizability

Let be a Banach lattice with order continuous norm, and let be a multiplicative semigroup of ideal-triangularizable positive compact operators on such that, for every pair , the atomic diagonal of the commutator is equal to zero. We prove that the semigroup is ideal-triangularizable.

On the positive commutator in the radical

In this paper we prove that a positive commutator between a positive compact operator A and a positive operator B is in the radical of the Banach algebra generated by A and B. Furthermore, on every at least three-dimensional Banach lattice we construct finite rank operators A and B satisfying

The countable sup property for lattices of continuous functions

AB\ge BA\ge 0

More on positive commutators

AB≥BA≥0 such that the commutator

Unbounded norm topology beyond normed lattices

AB-BA

Metrizability of minimal and unbounded topologies

AB-BA is not contained in the radical of the Banach algebra generated by A and B. These two results now completely answer to two open questions published in (Bračič et al., Positivity 14:431–439, 2010). We also obtain relevant results in the case of the Volterra and the Donoghue operator.