Isometries of absolute order unit spaces

Positivity - We prove that a unital, bijective linear map between absolute order unit spaces is an isometry if and only if it is absolute value preserving. We deduce that, on (unital) JB-algebras,...     

Compact operators which factor through subspaces of lp

Let 1 ≤ p ≤ ∞. A subset K of a Banach space X is said to be relatively p ‐compact if there is an 〈x_n 〉 ∈ l^s _p (X) such that for every k ∈ K there is an 〈α_n 〉 ∈ l_{p ′} such that k = σ^∞_n=1 α_n x_n . A linear operator T: X → Y is said to be p ‐compact if T (Ball (X)) is relatively p ‐compact in Y. The set of all p ‐compact operators K_p (X, Y) from X to Y is a Banach space with a suitable factorization norm κ_p and (K_p , κ_p ) is a Banach operator ideal. In this paper we investigate the dual operator ideal (K^d _p , κ^d _p ). It is shown that κ^d _p (T) = π_p (T) for all T ∈ B (X, Y) if either X or Y is finite‐dimensional. As a consequence it is proved that the adjoint ideal of K^d _p is I_{p ′}, the ideal of p ′‐integral operators. Further, a composition/decomposition theorem K^d _p = Π_p K is proved which also yields that (Π^min _p )^inj = K^d _p . Finally, we discuss the density of finite rank operators in K^d _p and give some examples for different values of p in this respect. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Corrigendum to the paper ``Adjoining an Order Unit to a Matrix Ordered Space'

An error has been detected (and also corrected) in Theorem 2.8 of the paper entitled “Adjoining an Order Unit to a Matrix Ordered Space” (Positivity, (2005)9: 207–223; DOI ). Accordingly, some of the results of the paper have been modified. Also, a notion of C*-matricially, Riesz normed spaces has been introduced.     

Isolation of the novel dirhodium(II/II) thiolate compound Rh(2)(eta(1)-C(6)H(5)S)(2)(mu-C(6)H(5)S)(2)(bpy)(2)

The reaction of the anticancer active compound [Rh(2)(mu-O(2)CCH(3))(2)(bpy)(2)(CH(3)CN)(2)][BF(4)](2) (1) (bpy = 2,2'-bipyridine) with NaC(6)H(5)S under anaerobic conditions yields Rh(2)(eta(1)-C(6)H(5)S)(2)(mu-C(6)H(5)S)(2)(bpy)(2).CH(3)OH (2), which was characterized by UV-visible, IR, and (1)H NMR spectroscopies as well as single-crystal X-ray crystallography. Compound 2 crystallizes as dark red platelets in the monoclinic space group C2/c with cell parameters a = 20.398(4) A, b = 11.861(2) A, c = 17.417(4) A, beta = 108.98 degrees, V = 3984.9(14) A(3), Z = 4. The main structural features are the presence of a [Rh(2)](4+) core with a Rh-Rh distance of 2.549(2) A bridged by two benzene thiolate ligands in a butterfly-type arrangement. The axial positions of the [Rh(2)](4+) core are occupied by two terminal benzene thiolates. Cyclic voltammetric studies of 2 reveal that the compound exhibits an irreversible oxidation at +0.046 V in CH(3)CN, which is in accord with the fact that the compound readily oxidizes in the presence of O(2). The fact that this unusual dirhodium(II/II) thiolate compound is formed under these conditions is an important first step in understanding the metabolism of dirhodium anticancer active compounds with thiol-containing peptides and proteins.     

The effect of a cavity on airfoil tones

The presence of a cavity in the pressure surface of an airfoil has been found via experiment to play a role in the production of airfoil tones, which was attributed to the presence of an acoustic feedback loop. The cavity length was sufficiently small that cavity oscillation modes did not occur for most of the investigated chord-based Reynolds number range of 70,000–320,000. The airfoil tonal noise frequencies varied as the position of the cavity was moved along a parallel section at the airfoil's maximum thickness: specifically, for a given velocity, the frequency spacing of the tones was inversely proportional to the geometric distance between the cavity and the trailing edge. The boundary layer instability waves considered responsible for the airfoil tones were only detected downstream of the cavity. This may be the first experimental verification of these aspects of the feedback loop model for airfoil tonal noise.     

On diquark clusters in a quark-gluon plasma

An attempt is made to account for the effect of the size of a diquark in exploring the possibility that the pairs of quarks will form diquark clusters in a quark-gluon plasma. It is found that the extended scalar diquarks are distributed more uniformly in the spatial volume than the point diquarks. Although the qualitative features of the pressure-energy density curve remain more or less the same except for small values of energy density, but there appears further lowering of the diquark gas energy in the present case as compared not only to that of the point diquark but also of a free quark gas.     

Momentum- and energy-dependence ofJ/Ψ suppression in relativistic heavy ion collisions

With a view to understand the available data on the momentum- and energy-dependences of theJ/Ψ suppression, we compute the suppression rate within the framework of a hydrodynamical evolution model for the quark-gluon plasma (QGP) formation. We make use of an ansatz for the temperature profile function which accounts not only for the space and time evolutions of QGP but also for the possibility of a mixed phase in the boundary region of the deconfined phase. While the predictions are made for the longitudinal momentum- and energy-dependences of the suppression rate, a satisfactory agreement with the available data is found for its dependences on the transverse momentum and the transverse energy.     

Orthogonality in $$C^{*}$$-algebras

The aim in this paper is to study algebraic orthogonality between positive elements of a \(C^{*}\)-algebra in the context of geometric orthogonality. It has been shown that the algebraic orthogonality in certain classes of \(C^{*}\)-algebras is equivalent to geometric orthogonality when supported with some order-theoretic conditions. Further more, algebraic orthogonality between positive elements in a \(C^{*}\)-algebra is also characterized in terms of positive linear functionals.