The Essential Norm of Operators on Aαp(Bn)A^p_\alpha(\mathbb{B}_n)

In this paper we characterize the compact operators on $A^p_\alpha(\mathbb{B}_n)$ when $1-1$. The main result shows that an operator on $A^p_\alpha(\mathbb{B}_n)$ is compact if and only if it belongs to the Toeplitz algebra and its Berezin transform vanishes on the boundary of the ball.Comment: v1: 32 pages; v2: 32 pages, typos corrected; v3: 32 pages, typos corrected, presentation improved based on referee comment

Analysis of Quiet-Sun Internetwork Magnetic Fields Based on Linear Polarization Signals

We present results from the analysis of Fe I 630 nm measurements of the quiet Sun taken with the spectropolarimeter of the Hinode satellite. Two data sets with noise levels of 1.2{\times}10-3 and 3{\times}10-4 are employed. We determine the distribution of field strengths and inclinations by inverting the two observations with a Milne-Eddington model atmosphere. The inversions show a predominance of weak, highly inclined fields. By means of several tests we conclude that these properties cannot be attributed to photon noise effects. To obtain the most accurate results, we focus on the 27.4% of the pixels in the second data set that have linear polarization amplitudes larger than 4.5 times the noise level. The vector magnetic field derived for these pixels is very precise because both circular and linear polarization signals are used simultaneously. The inferred field strength, inclination, and filling factor distributions agree with previous results, supporting the idea that internetwork fields are weak and very inclined, at least in about one quarter of the area occupied by the internetwork. These properties differ from those of network fields. The average magnetic flux density and the mean field strength derived from the 27.4% of the field of view with clear linear polarization signals are 16.3 Mx cm-2 and 220 G, respectively. The ratio between the average horizontal and vertical components of the field is approximately 3.1. The internetwork fields do not follow an isotropic distribution of orientations.Comment: To appear in APJ, Vol 749, 201

Universality in the transport response of molecular wires physisorbed onto graphene electrodes

We analyze the low-voltage transport response of large molecular wires bridging graphene electrodes, where the molecules are physisorbed onto the graphene sheets by planar anchor groups. In our study, the sheets are pulled away to vary the gap length and the relative atomic positions. The molecular wires are also translated in directions parallel and perpendicular to the sheets. We show that the energy position of the Breit-Wigner molecular resonances is universal for a given molecule, in the sense that it is independent of the details of the graphene edges, gaps lengths or of the molecule positions. We discuss the need to converge carefully the k-sampling to provide reasonable values of the conductance.Comment: 6 pages, 6 figure