COPIES OF c(0)(Gamma) IN C(K, X) SPACES

We extend some results of Rosenthal, Cembranos, Freniche, E. Saab-P. Saab and Ryan to study the geometry of copies and complemented copies of c(0)(Gamma) in the classical Banach spaces C(K, X) in terms of the carclinality of the set Gamma, of the density and caliber of K and of the geometry of X and its dual space X*. Here are two sample consequences of our results: (1) If C([0, 1], X) contains a copy of c(0)(N-1), then X contains a copy of c(0)(N-1). (2) C(beta N, X) contains a complemented copy of c(0)(N-1) if and only if X contains a copy of c(0)(N-1). Some of our results depend on set-theoretic assumptions. For example, we prove that it is relatively consistent with ZFC that if C(K) contains a copy of c(0)(N-1) and X has dimension NI, then C(K, X) contains a complemented copy of cc(0)(N-1).

Suppression of Hypoxia-Inducible Factor-1 alpha Contributes to the Antiangiogenic Activity of Red Propolis Polyphenols in Human Endothelial Cells

Polyphenol-enriched fractions from natural sources have been proposed to interfere with angiogenesis in pathological conditions. We recently reported that red propolis polyphenols (RPP) exert antiangiogenic activity. However, molecular mechanisms of this activity remain unclear. Here, we aimed at characterizing molecular mechanisms to explain the impact of RPP on endothelial cells' (EC) physiology. We used in vitro and ex and in vivo models to test the hypothesis that RPP inhibit angiogenesis by affecting hypoxia-inducible factor-1 alpha (HIF1 alpha) stabilization in EC. RPP (10 mg/L) affected angiogenesis by reducing migration and sprouting of EC, attenuated the formation of new blood vessels, and decreased the differentiation of embryonic stem cells into CD31-positive cells. Moreover, RPP (10 mg/L) inhibited hypoxia- or dimethyloxallylglycine-induced mRNA and protein expression of the crucial angiogenesis promoter vascular endothelial growth factor (VEGF) in a time-dependent mariner. Under hypoxic conditions, RPP at 10 mg/L, supplied for 1-4 h, decreased HIF1 alpha protein accumulation, which in turn attenuated VEGF gene expression. In addition, RPP reduced the HIF1 alpha protein half-life from similar to 58 min to 38 min under hypoxic conditions. The reduced HIF1 alpha protein half-life was associated with an increase in the von Hippel-Lindau (pVHL)-dependent proteasomal degradation of HIF1 alpha. RPP (10 mg/L, 4 h) downregulated Cdc42 protein expression. This caused a corresponding increase in pVHL protein levels and a subsequent degradation of HIF1 alpha. In summary, we have elucidated the underlying mechanism for the antiangiogenic action of RPP, which attenuates HIF1 alpha protein accumulation and signaling. J. Nutr. 142: 441-447, 2012.