Extensions of homogeneous polynomials ON c(0)(l(2)(i))

We show that a 2-homogeneous polynomial on the complex Banach space c(0)(l(2)(i)) is norm attaining if and only if it is finite (i.e, depends only on finite coordinates). As the consequence, we show that there exists a unique norm-preserving extension for norm-attaining 2-homogeneous polynomials on c(0)(l(2)(i)).

L-(2-Quinolyl)-2-naphthol: A new intra-intermolecular photoacid-photobase molecule

Photochemical and photophysical properties of 1-(2-quinolyl)-2-naphthol (2QN) in water and organic solvents, as well in glassy media were studied to investigate the occurrence of intramolecular excited state prototropic reactions between the naphthol and quinoline rings. Spectral data show the two chromophores apparently behaving independently. However, in acid aqueous media or in low polarity solvents a new electronic transition red shifted band with respect to that of the parent compounds assigned to an intramolecular H-bond and to a quinoid form, respectively, shows up. Model calculations and R-X data lend support to a minimum energy conformer having a dihedral angle of similar to 39 degrees between the two groups. Singlet excited state properties (S-1) show a high suppressive effect of one ring over the other, resulting in very low emission yields at room temperature. The occurrence of excited state intramolecular proton transfer is observed in water (zwitter ion form) and in low polarity media (quinoid form) and originates from a previously CT H-bonded state. Phosphorescence data allowed a reasonable description of the electronic states of 2QN. In addition two new derivatives were prepared having the N atom blocked by methylation and both the N and O groups blocked by a CH2 bridge. The spectral data of these two compounds confirmed the attributions made for 2QN. (C) 2007 Elsevier B.V. All rights reserved.