Operator algebras and a theorem of Dieudonne

LetA be aC*-algebra with second dualA″. Let (φ _n)(n=1,...) be a sequence in the dual ofA such that limφ _n(a) exists for eacha εA. In general, this does not imply that limφ _n(x) exists for eachx εA″. But if limφ _n(p) exists whenever p is the range projection of a positive self-adjoint element of the unit ball ofA, then it is shown that limφ _n(x) does exist for eachx inA″. This is a non-commutative generalisation of a celebrated theorem of Dieudonné. A new proof of Dieudonné’s theorem, for positive measures, is given here. The proof of the main result makes use of Dieudonné’s original theorem.     

Selective Targeting of Dendritic Cell‐Specific Intercellular Adhesion Molecule‐3‐Grabbing Nonintegrin (DC‐SIGN) with Mannose‐Based Glycomimetics: Synthesis and Interaction Studies of Bis(benzylamide) Derivatives of a Pseudomannobioside

Dendritic cell‐specific intercellular adhesion molecule‐3‐grabbing nonintegrin (DC‐SIGN) and Langerin are C‐type lectins of dendritic cells (DCs) that share a specificity for mannose and are involved in pathogen recognition. HIV is known to use DC‐SIGN on DCs to facilitate transinfection of T‐cells. Langerin, on the contrary, contributes to virus elimination; therefore, the inhibition of this latter receptor is undesired. Glycomimetic molecules targeting DC‐SIGN have been reported as promising agents for the inhibition of viral infections and for the modulation of immune responses mediated by DC‐SIGN. We show here for the first time that glycomimetics based on a mannose anchor can be tuned to selectively inhibit DC‐SIGN over Langerin. Based on structural and binding studies of a mannobioside mimic previously described by us ( 2 ), a focused library of derivatives was designed. The optimized synthesis gave fast and efficient access to a group of bis(amides), decorated with an azide‐terminated tether allowing further conjugation. SPR inhibition tests showed improvements over the parent pseudomannobioside by a factor of 3–4. A dimeric, macrocyclic structure ( 11 ) was also serendipitously obtained, which afforded a 30‐fold gain over the starting compound ( 2 ). The same ligands were tested against Langerin and found to exhibit high selectivity towards DC‐SIGN. Structural studies using saturation transfer difference NMR spectroscopy (STD‐NMR) were performed to analyze the binding mode of one representative library member with DC‐SIGN. Despite the overlap of some signals, it was established that the new ligand interacts with the protein in the same fashion as the parent pseudodisaccharide. The two aromatic amide moieties showed relatively high saturation in the STD spectrum, which suggests that the improved potency of the bis(amides) over the parent dimethyl ester can be attributed to lipophilic interactions between the aromatic groups of the ligand and the binding site of DC‐SIGN.     

Radial oscillations of neutron stars in strong magnetic fields

The eigen frequencies of radial pulsations of neutron stars are calculated in a strong magnetic field. At low densities we use the magnetic BPS equation of state (EOS) similar to that obtained by Lai and Shapiro while at high densities the EOS obtained from the relativistic nuclear mean field theory is taken and extended to include strong magnetic field. It is found that magnetized neutron stars support higher maximum mass whereas the effect of magnetic field on radial stability for observed neutron star masses is minimal.