We study morphisms of the generalized quantum logic tripotents in JBW $$^*$$ -triples and von Neumann algebras. Especially, we establish a generalization celebrated Dye’s theorem on orthoisomorphisms between lattices to this new context. show existence one-to-one correspondence following maps: (1) posets preserving reflection $$u\rightarrow - u$$ (2) maps triples that preserve are real linear s...

We investigate the effect of structure-preserving perturbations on the solution to a linear system, matrix inversion, and distance to singularity. Particular attention is paid to linear and nonlinear structures that form Lie algebras, Jordan algebras and automorphism groups of a scalar product. These include complex symmetric, pseudo-symmetric, persymmetric, skewsymmetric, Hamiltonian, unitary,...

We determine the symmetries and reversing symmetries within G, the group of real planar polynomial automorphisms, of area-preserving nonlinear polynomial maps L in generalised standard form, L : x = x + p1(y) , y ′ = y + p2(x ) , where p1 and p2 are polynomials. We do this by using the amalgamated free product structure of G. Our results lead to normal forms for polynomial maps in generalised s...

Denote by B(H) the Banach algebra of all bounded linear operators on a complex Hilbert space H. Let A ∈ B(H), and denote by σ(A) the spectrum of A. For ε > 0, define the ε-pseudospectrum σε(A) of A as σε(A) = {z ∈ σ(A+ E) : E ∈ B(H), ∥E∥ < ε}. In this paper, the pseudospectra of several special classes of operators are characterized. As an application, complete descriptions are given of the map...

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...

Let Φ be a trace-preserving, positivity-preserving linear map on the algebra of complex 2 × 2 matrices, and let Ω be any finite-dimensional completely positive map. For p = 2 and p ≥ 4, we prove that the maximal p-norm of the product map Φ⊗Ω is the product of the maximal p-norms of Φ and Ω. Restricting Φ to the class of completely positive maps, this settles the multiplicativity question for al...