Unbounded Disjointness Preserving Linear Functionals

Lawrence G. Brown, Ngai-Ching Wong
2004 Monatshefte für Mathematik (Print)  
Let X be a locally compact Hausdorff space and C 0 (X) the Banach space of continuous functions on X vanishing at infinity. In this paper, we shall study unbounded disjointness preserving linear functionals on C 0 (X). They arise from prime ideals of C 0 (X), and we translate it into the cozero set ideal setting. In particular, every unbounded disjointness preserving linear functional of c 0 can be constructed explicitly through an ultrafilter on N complementary to a cozero set ideal. This
more » ... filter method can be extended to produce many, but in general not all, such functionals on C 0 (X) for arbitrary X. We also make some remarks where C 0 (X) is replaced by a non-commutative C*-algebra.
doi:10.1007/s00605-003-0045-2 fatcat:ihu63qm2nvgqrafdjlqfclwkqe