One of unsolved problems in quantum measurement theory is to characterize coexistence of quantum effects. In this paper, applying positive operator matrix theory, we give a mathematical characterization of the witness set of coexistence of quantum effects and obtain a series of properties of coexistence. We also devote to characterizing bijective morphisms on quantum effects leaving the witness...

In this paper, we focus on the structured multi-frame vectors in Hilbert $C^*$-modules. More precisely, it will be shown that the set of all complete multi-frame vectors for a unitary system can be parameterized by the set of all surjective operators, in the local commutant. Similar results hold for the set of all complete wandering vectors and complete multi-Riesz vectors, when the surjective ...

In this paper, we investigate the concept of topological stationary for locally compact semigroups. In [4], T. Mitchell proved that a semigroup S is right stationary if and only if m(S) has a left Invariant mean. In this case, the set of values ?(f) where ? runs over all left invariant means on m(S) coincides with the set of constants in the weak* closed convex hull of right translates of f. Th...

In [1], the wave functions of quantum trigonometric n-particle Ruijsenaars model are defined as matrix elements of operators of representations of Cartan subalgebra between vectors invariant with respect to q-deformation U ′ q(son) of Lie algebra so(n). It was shown there, that the wave functions defined in such a way are simultaneous eigenfunctions of commuting set of Macdonald–Ruijsenaars dif...

We show that each power bounded operator with spectral radius equal to one on a reflexive Banach space has a nonzero vector which is not supercyclic. Equivalently, the operator has a nontrivial closed invariant homogeneous subset. Moreover, the operator has a nontrivial closed invariant cone if 1 belongs to its spectrum. This generalizes the corresponding results for Hilbert space operators. Fo...

This paper concerns the problem of output consensus in nonlinear non-minimum phase systems. The main contribution of the paper is to guarantee achieving consensus in the presence of unstable zero dynamics. To achieve this goal, an output redefinition method is proposed. The new outputs of agents are functions of original outputs and internal states and defined such that the dynamics of agents a...

in this paper, we investigate the concept of topological stationary for locally compact semigroups. in [4], t. mitchell proved that a semigroup s is right stationary if and only if m(s) has a left invariant mean. in this case, the set of values ?(f) where ? runs over all left invariant means on m(s) coincides with the set of constants in the weak* closed convex hull of right translates of f. th...

Interactions in complex solutions that consist of multiple components can be quantified via number correlations observed within an isochoric subsystem. The fluctuation solution theory carries out a conversion between experimental data (usually measured under isobaric conditions) and the through cumbersome thermodynamic variable transformations. In contrast, we have recently demonstrated heurist...