Commutators with finite spectrum
The purpose of this paper is to study derivations d, d′ defined on a Banach algebra A such that the spectrum σ([dx,d′x]) is finite for all x ∈ A. In particular we show that if the algebra is semisimple, then there exists an element a in the socle of A such that [d,d′] is the inner derivation implemented by a.
The image of a derivation is contained in the radical
In 1955 I. M. Singer and J. Wermer proved that a bounded derivation on a commutative Banach algebra maps into the (Jacobson) radical; they conjectured that this result holds even if the derivation is unbounded. We give a proof of this conjecture. The central idea in the proof is the introduction of the concept of a recalcitrant system of elements in a commutative radical Banach algebra. Such systems put algebraic constraints upon a derivation which prevent the derivation from mapping outside of the radical.
PUBLIC PARTICIPATION AND SOCIAL ACCEPTABILITY IN THE PHILIPPINE EIA PROCESS
Since 1992, the Philippines has employed an innovative requirement to demonstrate social acceptability in project planning as a means through which public participation can be established. This paper discusses the participatory mechanisms used and evaluates the effectiveness of public participation in three case studies from key development sectors. In doing so, the existing conceptual frameworks for evaluating public participation are further developed through insights to community empowerment and sustainability in particular. Whilst increased public participation has resulted in improvements in the EIA process and environmental decision making in the Philippines, the evaluation of the case studies also reveals substantial issues of conflict within the communities and of the representation of diverse local interests at core stages in the planning process.