Related papers: Fixed points of commutative L\"uders operations
A well-known theorem due to R. E. Curto and N. Salinas gives a necessary and sufficient condition for the unitary equivalence of commuting tuples of bounded linear operators acting on reproducing kernel Hilbert spaces. Inspired by this…
We call an operator algebra A {\em reversible} if A with reversed multiplication is also an abstract operator algebra (in the modern operator space sense). This class of operator algebras is intimately related to the {\em symmetric operator…
Actions of locally compact groups and quantum groups on W*-ternary rings of operators are discussed and related crossed products introduced. The results generalise those for von Neumann algebraic actions with proofs based mostly on passing…
Let $U$ be a unitary operator defined on some infinite-dimensional complex Hilbert space ${\cal H}$. Under some suitable regularity assumptions, it is known that a local positive commutation relation between $U$ and an auxiliary…
Quantum coherence as an important physical resource plays the key role in implementing various quantum tasks, whereas quantum coherence is often deteriorated due to the noise. In this paper, we analyse under which dynamical conditions the…
For a group $G$ of not prime power order, Oliver showed that the obstruction for a finite CW-complex $F$ to be the fixed point set of a contractible finite $G$-CW-complex is the Euler characteristic $\chi(F)$. He also has the similar…
We give a new proof of the result that if f and g are transcendental entire functions, then the composite function f(g) has infinitely many fixed points. The method yields a number of generalization of this result. In particular, it extends…
In this paper, we prove some common coupled fixed point theorems for mappings satisfying different contractive conditions in the context of complete $C^*$-algebra-valued metric spaces. Moreover, the paper provides an application to prove…
Let G be a group acting on the plane by orientation-preserving homeomorphisms. We show that if for some k>0 there is a ball of radius r > k/\sqrt{3} such that each point x in the ball satisfies |gx -hx| < k for all g, h in G, and the action…
We present coincidence and common fixed point results of selfmappings satisfying a contraction type in partially ordered metric spaces. As an application, we give an existence theorem for a common solution of integral equations.
The discrimination of quantum operations has long been an intriguing challenge, with theoretical research significantly advancing our understanding of the quantum features in discriminating quantum objects. This challenge is closely related…
The aim of this paper is to establish some metrical coincidence and common fixed point theorems with an arbitrary relation under an implicit contractive condition which is general enough to cover a multitude of well known contraction…
We study maps on the set of permutations of n generated by the R\'enyi-Foata map intertwined with other dihedral symmetries (of a permutation considered as a 0-1 matrix). Iterating these maps leads to dynamical systems that in some cases…
The usual position-momentum commutation relation plays a fundamental role in the mathematical description of continuous-variable quantum systems. In the case of a qudit described by a Hilbert space of a high enough dimension, there exists a…
Some beautiful identities involving hook contents of Young diagrams have been found in the field of quantum information processing, along with a combinatorial proof. We here give a representation theoretic proof of these identities and a…
In the consistent histories formulation of quantum theory, the probabilistic predictions and retrodictions made from observed data depend on the choice of a consistent set. We show that this freedom allows the formalism to retrodict…
Consider a commutative monoid $(M,+,0)$ and a biadditive binary operation $\mu \colon M \times M \to M$. We will show that under some additional general assumptions, the operation $\mu$ is automatically both associative and commutative. The…
In this paper, we present some fixed point theorems for operator systems in the line of Krasnosel'skii's theorem in cones. The cone-compression and cone-expansion type conditions are imposed in a component-wise manner. Unlike related…
We address the problem of unambiguous discrimination among a given set of quantum operations. The necessary and sufficient condition for them to be unambiguously distinguishable is derived in the cases of single use and multiple uses…
In a recent series of papers we have analyzed a certain deformation of the canonical commutation relations producing an interesting functional structure which has been proved to have some connections with physics, and in particular with…