arXiv subjects

Bogdan D. Djordjevic

Publications and source records attributed to Bogdan D. Djordjevic.

4 recordsLinked to original sources

arXiv2026

Commutator-based Solutions to $AXA = XAX$ when $A^n = tA^2$

This paper offers a novel analytical method for obtaining new non-commuting solutions for the Yang-Baxter-like matrix equation $AXA=XAX$, when the coefficient matrix $A$ satisfies the square-cyclic condition $A^n=tA^2$. All the consistency criteria are proved and the obtained results are demonstrated on worked examples. The findings provided by this article simultaneously generalize several existing special cases regarding this topic. Consequently, by employing the obtained results, the previously unstudied inhomogeneous Yang-Baxter matrix equation $AXA=XAX+B$ is solved when $A$ is either invertible, or satisfies $A^2=0$.

math.RA↗

arXiv2026

Variants of the Quantum Phase Operator for the Harmonic Oscillator

We introduce and study quantum phase operators associated with the Quantum Harmonic Oscillator (QHO). We show that these operators are trace-class perturbations of the Susskind-Glogower operators and examine their mathematical and physical properties. The construction is motivated by the physically relevant two-phase case.

quant-ph↗

arXiv2024

On representations and topological aspects of positive maps on non-unital quasi *-algebras

In this paper, we provide a representation of a certain class of C*-valued positive sesquilinear and linear maps on non-unital quasi *-algebras. Also, we illustrate our results on the concrete examples of non-unital Banach quasi *-algebras, such as the standard Hilbert module over a commutative C*-algebra, Schatten p-ideals, and noncommutative L2 spaces induced by a semifinite, nonfinite trace. As a consequence of our results, we obtain a representation of all bounded positive linear C*-valued maps on non-unital C*-algebras. We also deduce some norm inequalities for these maps. Finally, we consider a noncommutative L2 space equipped with the topology generated by a positive sesquilinear form and we construct a topologically transitive operator on this space.

math.OA↗

arXiv2024

Solutions to a system of Yang-Baxter matrix equations

In this article, a system of Yang-Baxter-type matrix equations is studied, $XAX=BXB$, $XBX=AXA$, which "generalizes" the matrix Yang-Baxter equation and exhibits a broken symmetry. We investigate the solutions of this system from various geometric and topological points of view. We analyze the existence of doubly stochastic solutions and intertwining solutions to the system and describe the conditions for their existence. Furthermore, we characterize the case when $A$ and $B$ are idempotent orthogonal complements. i.e., $A^2 =A, B^2= B, AB = BA =0$. We also completely characterize the set of solutions for $n=2$ using commutative algebraic techniques.

math.RA↗