54,282 research outputs found
Partial and Total Ideals of Von Neumann Algebras
A notion of partial ideal for an operator algebra is a weakening the notion
of ideal where the defining algebraic conditions are enforced only in the
commutative subalgebras. We show that, in a von Neumann algebra, the
ultraweakly closed two-sided ideals, which we call total ideals, correspond to
the unitarily invariant partial ideals. The result also admits an equivalent
formulation in terms of central projections. We place this result in the
context of an investigation into notions of spectrum of noncommutative
-algebras.Comment: 14 page
On the stability of spacelike hypersurfaces
In this paper we study the strong stability of spacelike hypersurfaces with
constant -th mean curvature in Generalized Robertson-Walker spacetimes of
constant sectional curvature. In particular, we treat the case in which the
ambient spacetime is the de Sitter space
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