论文标题
近似模块化：卡尔顿的常数不小于3
Approximate modularity: Kalton's constant is not smaller than 3
论文作者
论文摘要
卡尔顿和罗伯茨[译。阿米尔。数学。 Soc., 278 (1983), 803--816] proved that there exists a universal constant $K\leqslant 44.5$ such that for every set algebra $\mathcal{F}$ and every 1-additive function $f\colon \mathcal{F}\to \mathbb R$ there exists a finitely-additive signed measure $μ$ defined on $ \ MATHCAL {f} $使得$ | f（a）-μ（a）| \ leqslant k $用于\ Mathcal {f} $中的任何$ a \。 Pawlik [Colloq。 Math。，54（1987），163--164]，他证明该常数不小于$ 1.5 $；在非负1 addive函数上，我们将其提高到已经达到了$ 3 $。
Kalton and Roberts [Trans. Amer. Math. Soc., 278 (1983), 803--816] proved that there exists a universal constant $K\leqslant 44.5$ such that for every set algebra $\mathcal{F}$ and every 1-additive function $f\colon \mathcal{F}\to \mathbb R$ there exists a finitely-additive signed measure $μ$ defined on $\mathcal{F}$ such that $|f(A)-μ(A)|\leqslant K$ for any $A\in \mathcal{F}$. The only known lower bound for the optimal value of $K$ was found by Pawlik [Colloq. Math., 54 (1987), 163--164], who proved that this constant is not smaller than $1.5$; we improve this bound to $3$ already on a non-negative 1-additive function.
