Strong proximinality and intersection properties of balls in Banach spaces

We investigate a variation of the transitivity problem for proximinality properties of subspaces and intersection properties of balls in Banach spaces. For instance, we prove that if Z⊆Y⊆X, where Z is a finite co-dimensional subspace of X which is strongly proximinal in Y and Y is an M-ideal in X, then Z is strongly proximinal in X. Towards this, we prove that a finite co-dimensional proximinal subspace Y of X is strongly proximinal in X if and only if Y⊥⊥ is strongly proximinal in X**. We also prove that in an abstract L1-space, the notions of strongly subdifferentiable points and quasi-polyhedral points coincide. We also give an example to show that M-ideals need not be ball proximinal. Moreover, we prove that in an L1-predual space, M-ideals are ball proximinal

Ideal operators and relative Godun sets

In this paper we study ideals in Banach spaces through ideal operators. We provide characterisation of recently introduced notion of almost isometric ideal which is a version of Principle of Local Reexivity for a subspace of a Banach space. Studying ideals through ideal operators give us better insight in to the properties of these subspaces vis-a-vis properties of the space itself. We provide a few applications of our characterisation theorem.The National Board for Higher Mathematics (NBHM) of India. (No.2/40(2)/2014/R&D-II/6252).peerReviewe

The unusual persistence of an ozone hole over a southern mid-latitude station during the Antarctic spring 2009: a multi-instrument study

International audienceRecord-low ozone column densities (with a minimum of 212 DU) persisted over three weeks at the Río Gallegos NDACC (Network for the Detection of Atmospheric Composition Change) station (51.5° S, 69.3° W) in November 2009. Total ozone remained two standard deviations below the climatological mean for five consecutive days during this period. The statistical analysis of 30 years of satellite data from the Multi Sensor Reanalysis (MSR) database for Río Gallegos revealed that such a long-lasting low-ozone episode is a rare occurrence. The event is examined using height-resolved ozone lidar measurements at Río Gallegos, and observations from satellite and ground-based instruments. The computed relative difference between the measured total ozone and the climatological monthly mean shows reductions varying between 10 and 30% with an average decrease of 25%. The mean absolute difference of total ozone column with respect to climatological monthly mean ozone column is around 75 DU. Extreme values of the UV index (UVI) were measured at the ground for this period, with the daily maximum UVI of around 13 on 15 and 28 November. The high-resolution MIMOSA-CHIM (Modélisation Isentrope du transport Méso-échelle de l'Ozone Stratosphérique par Advection) model was used to interpret the ozone depletion event. An ozone decrease of about 2 ppmv was observed in mid-November at the 550 K isentropic level (~22 km). The position of Río Gallegos relative to the polar vortex was classified using equivalent latitude maps. During the second week of November, the vortex was over the station at all isentropic levels, but after 20 November and until the end of the month, only the 10 lower levels in the stratosphere were affected by vortex overpasses with ozone poor air masses. A rapid recovery of the ozone column density was observed later, due to an ozone rich filament moving over Río Gallegos between 18 and 24 km in the first two weeks of December 2009