Subspaces discerning nullcontinuity

Details Subspaces discerning nullcontinuity Subspaces discerning nullcontinuity

2004-12-10

arxiv.org/abs/math/0412210v1

Mathematics

Functional Analysis

Scientific paper

Given positive linear functional l on a vector lattice L of real functions, and a vector subspace M of L, we construct a vector subspace P(M) of M in such a way that 1) l is nullcontinuous on P(M), and 2) if l is nullcontinuous on M then P(M) is all of M. We mention here that this result continues to hold for quite general modes of convergence, including tau-continuity. Our construction uses a new method involving the "kernel" of a seminorm.

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