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We study 1-complemented subspaces of the sequence spaces ℓ1 andc 0. In ℓ1, 1-complemented subspaces of codimensionn are those which can be obtained as intersection ofn 1-complemented hyperplanes. Inc 0, we prove a characterization of 1-complemented subspaces of finite codimension in terms of intersection of hyperplanes.
Abstract
Some results on existence of norm one projections onto hyperplanes in spaces with a Schauder basis are given. Possible characterizations of Hilbert spaces using this property are also discussed.
Amongst all terrestrial ecosystems, the productivity of Mediterranean-type ecosystems has been suggested to be one of the most responsive to increasing atmospheric CO 2 . The extent to which this prediction holds will depend in part on plant responses to elevated CO 2 under the highly variable conditions characteristic of semiarid regions. Structure and composition responses of a semi-natural grassland community to a step-increase in atmospheric CO 2 (to about 580 μmol mol −1 ) were examined in the field using Free-Air CO 2 Enrichment (FACE) under seasonally varying moisture conditions. The limited production response to elevated concentrations of atmospheric CO 2 of this grassland community was counterbalanced by the effect on the phenology of many species. These findings suggest that predictions regarding Mediterranean plant responses to elevated CO 2 should account for seasonal patterns of production regulatory responses, which may vary across species and plant functional types.
