Summability and estimates for polynomials and multilinear mappings

In this paper we extend and generalize several known estimates for homogeneous polynomials and multilinear mappings on Banach spaces. Applying the theory of absolutely summing nonlinear mappings, we prove that estimates which are known for mappings on ?_p spaces in fact hold true for mappings on arbitrary Banach spaces.     

A polynomial Hutton theorem with applications

Extending a classical linear result due to Hutton to a nonlinear setting, we prove that a continuous homogeneous polynomial between Banach spaces can be approximated by finite rank polynomials if and only if its adjoint can be approximated by finite rank linear operators. Among other consequences, we apply this result to generalize a classical result due to Aron and Schottenloher about the approximation property on spaces of polynomials and a recent result due to Çaliskan and Rueda about the quasi-approximation property on projective symmetric tensor products.     

Luminescence quantum yield determination for molecules adsorbed onto solid powdered particles.

A new methodology for the determination of the fluorescence quantum yield of dyes adsorbed onto microcrystalline cellulose is presented and applied to rhodamine 101, cresyl violet and auramine O. It is based on a previously reported method by Ruetten and Thomas (J. Phys. Chem., 1998, 102, 598-606), which is not applicable to the dyes used in the present study. It uses ground-state diffuse reflectance spectra obtained with and without filters, which prevents the luminescence of the dye from reaching the integrating sphere and the photodetector. New equations are presented here, correcting for the fluorescence emission of the dye, which depends on the detector sensitivity. Cut-on filters, which have a transmittance close to unity in the absorption region, and close to zero in the emission region, of the dye are used to obtain corrected reflectance spectra. The influence of the substrate was also taken into account. This methodology may be applied to other probes and surfaces or emissions of a different nature (i.e., phosphorescence or delayed fluorescence), and constitutes a very simple and general procedure to solve the important problem of luminescence quantum yield determination of probes adsorbed onto solid powdered surfaces.     

When every multilinear mapping is multiple summing

In this paper we give a systematized treatment to some coincidence situations for multiple summing multilinear mappings which extend, generalize and simplify the methods and results obtained thus far. The application of our general results to the pertinent particular cases gives several new coincidences as well as easier proofs of some known results (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Cotype and absolutely summing linear operators

New applications of cotype to the theory of absolutely summing linear operators between Banach spaces are proved in this paper. Among other consequences we extend/complement some classical results of Bennett (Duke Math J 44:603?C639, 1977) on the existence of non-absolutely summing operators between ? _p spaces and of Davis and Johnson (Stud Math 51:81?C85, 1974) on the existence of compact non-absolutely summing linear operators. We also point out that some of our results are sharp.     

Radioresistance studies in Methylobacterium spp.

Methylobacterium extorquen was isolated and was found as one of the most resistant microorganisms in the original bioburden of ophthalmic cotton dressings to be submitted to γ radiation sterilization. Radiation survival curves were simultaneously performed in phosphate buffer and in test-pieces on two isolates, one obtained before irradiation (wild strain) and the other after irradiation at 20 kGy (rad strain), as well as on three type strains of Methylobacterium spp. (M. extorquens^T, M. radiotolerans^T and M. fujisawaense^T). The radiation resistance was compared using D_values. To analyze the effect of non linearity on radioresistance other measures were applied, such as intercept point, fraction of surviving cells at a selected dose and area. The ranking of strains with these approaches showed to be different, pointing out the need of an integrated measure of radioresistance. Therefore, an index of relative survival (IRS) is proposed.     

Scalar-valued dominated polynomials on Banach spaces

It is well known that 2-homogeneous polynomials on -spaces are 2-dominated. Motivated by the fact that related coincidence results are possible only for polynomials defined on symmetrically regular spaces, we investigate the situation in several classes of symmetrically regular spaces. We prove a number of non-coincidence results which makes us suspect that there is no infinite dimensional Banach space such that every scalar-valued homogeneous polynomial on is -dominated for every .

     

Algebraic reflexivity of sets of bounded operators on vector valued Lipschitz functions

In this paper we establish algebraic reflexivity properties of subsets of bounded linear operators acting on spaces of vector valued Lipschitz functions. We also derive a representation for the generalized bi-circular projections on these spaces.     

A unified Pietsch domination theorem

In this paper we prove an abstract version of Pietsch's domination theorem which unify a number of known Pietsch-type domination theorems for classes of mappings that generalize the ideal of absolutely p-summing linear operators. A final result shows that Pietsch-type dominations are totally free from algebraic conditions, such as linearity, multilinearity, etc.