GEOMETRIC RELATIONS BETWEEN SPACES OF NUCLEAR OPERATORS AND SPACES OF COMPACT OPERATORS

We extend and provide a vector-valued version of some results of C. Samuel about the geometric relations between the spaces of nuclear operators N(E, F) and spaces of compact operators K(E, F), where E and F are Banach spaces C(K) of all continuous functions defined on the countable compact metric spaces K equipped with the supremum norm. First we continue Samuel's work by proving that N(C(K-1), C(K-2)) contains no subspace isomorphic to K(C(K-3), C(K-4)) whenever K-1, K-2, K-3 and K-4 are arbitrary infinite countable compact metric spaces. Then we show that it is relatively consistent with ZFC that the above result and the main results of Samuel can be extended to C(K-1, X), C(K-2,Y), C(K-3, X) and C(K-4, Y) spaces, where K-1, K-2, K-3 and K-4 are arbitrary infinite totally ordered compact spaces; X comprises certain Banach spaces such that X* are isomorphic to subspaces of l(1); and Y comprises arbitrary subspaces of l(p), with 1 < p < infinity. Our results cover the cases of some non-classical Banach spaces X constructed by Alspach, by Alspach and Benyamini, by Benyamini and Lindenstrauss, by Bourgain and Delbaen and also by Argyros and Haydon.

Science and Society: The Case of Acceptance of Newtonian Optics in the Eighteenth Century

The present paper presents a historical study on the acceptance of Newton's corpuscular theory of light in the early eighteenth century. Isaac Newton first published his famous book Opticks in 1704. After its publication, it became quite popular and was an almost mandatory presence in cultural life of Enlightenment societies. However, Newton's optics did not become popular only via his own words and hands, but also via public lectures and short books with scientific contents devoted to general public (including women) that emerged in the period as a sort of entertainment business. Lectures and writers stressed the inductivist approach to the study of nature and presented Newton's ideas about optics as they were consensual among natural philosophers in the period. The historical case study presented in this paper illustrates relevant aspects of nature of science, which can be explored by students of physics on undergraduate level or in physics teacher training programs.

The nature of extremely red galaxies in the local universe

We investigate the nature of extremely red galaxies (ERGs), objects whose colours are redder than those found in the red sequence present in colour–magnitude diagrams of galaxies. We selected from the Sloan Digital Sky Survey Data Release 7 a volume-limited sample of such galaxies in the redshift interval 0.010 < z < 0.030, brighter than Mr = −17.8 (magnitudes dereddened, corrected for the Milky Way extinction) and with (g − r) colours larger than those of galaxies in the red sequence. This sample contains 416 ERGs, which were classified visually. Our classification was cross-checked with other classifications available in the literature. We found from our visual classification that the majority of objects in our sample are edge-on spirals (73 per cent). Other spirals correspond to 13 per cent, whereas elliptical galaxies comprise only 11 per cent of the objects. After comparing the morphological mix and the distributions of Hα/Hβ and axial ratios of ERGs and objects in the red sequence, we suggest that dust, more than stellar population effects, is the driver of the red colours found in these extremely red galaxies.