Geometry in preduals of spaces of 2-homogeneous polynomials on Hilbert spaces

Let H be a (real or complex) Hilbert space. Using spectral theory and properties of the Schatten–Von Neumann operators, we prove that every symmetric tensor of unit norm in HoH is an infinite absolute convex combination of points of the form xox with x in the unit sphere of the Hilbert space. We use this to obtain explicit characterizations of the smooth points of the unit ball of HoH .

Positive dilations of piecewise monotonic Markov maps

We provide an explicit formula which gives natural extensions of piecewise monotonic Markov maps defined on an interval of the real line. These maps are exact endomorphisms and define chaotic discrete dynamical systems.

Increased anti-tumour efficacy of doxorubicin when combined with sulindac in a xenograft model of an MRP-1-positive human lung cancer

Background: A number of cellular proteins, including P-glycoprotein (P-gp) and Multiple drug Resistance Protein (MRP-1), act as drug efflux pumps and are important in the resistance of many cancers to chemotherapy. We previously reported that a small number of NSAIDs could inhibit the activity of MRP-1. Materials and Methods: We chose sulindac as a candidate agent for further investigation as it has the most favourable efficacy and toxicity profile of the agents available for a potential specific MRP-1 inhibitor. NCI H460 cells expressed MRP-1 protein (by Western blot) and also the toxicity, of doxorubicin (a substrate of MRP-1) could be potentiated in this line using non-toxic concentrations of the MRP-1 substrate/inhibitor sulindac. These cells were implanted in nude mice and the animals divided into various groups which were administered doxorubicin and/or sulindac. Results: Sulindac was shown to significantly potentiate the tumour growth inhibitor activity of doxorubicin in this MRP-1-overexpressing human tumour xenograft model. Conclusion: Sulindac may be clinically useful as an inhibitor of the MRP-1 cancer resistance mechanism.