arXiv subjects

Marko Kandić

Publications and source records attributed to Marko Kandić.

21 records · Page 2Linked to original sources

arXiv2016

Triangularizability of Families of Polynomially Compact Operators

A recent paper of Shemesh shows triangularizability of a pair $\{A, B\}$ of complex matrices satisfying the condition $A [A,B]=[A,B] B=0$, or equivalently, the matrices $A$ and $B$ commute with their product $A B$. In this paper we extend this result to polynomially compact operators on Banach spaces. The case when the underlying space is Hilbert and one of operators is normal is also studied. Furthermore, we consider families of polynomially compact operators whose iterated commutators of some fixed length are zero. We also obtain a structure result in the special case of a finite family of algebraic operators.

math.FA↗

arXiv2014

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 $AB\geq BA\geq 0$ such that the commutator $AB-BA$ 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 [4]. We also obtain relevant results in the case of the Volterra and the Donoghue operator.

math.FA↗

arXiv2013

From local to global ideal-triangularizability

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

math.FA↗