Unbounded Disjointness Preserving Linear Functionals
نویسندگان
چکیده
Let X be a locally compact Hausdorff space and C0(X) the Banach space of continuous functions on X vanishing at infinity. In this paper, we shall study unbounded disjointness preserving linear functionals on C0(X). They arise from prime ideals of C0(X), and we translate it into the cozero set ideal setting. In particular, every unbounded disjointness preserving linear functional of c0 can be constructed explicitly through an ultrafilter on N complementary to a cozero set ideal. This ultrafilter method can be extended to produce many, but in general not all, such functionals on C0(X) for arbitrary X. We also make some remarks where C0(X) is replaced by a non-commutative C*-algebra.
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