论文标题
通勤收缩的联合和双串联
Joint and double coboundaries of commuting contractions
论文作者
论文摘要
让$ t $和$ s $是在Banach Space $ x $上通勤收缩。 $（i-t）（i-s）x $的元素称为{\ it double coboundaries}，$（i-t）x \ cap（i-s）x $的元素称为{\ it int intoct contint cobundaries}。对于$ u $和$ v $，通过通勤可转让的措施保留转换，从而产生了Aperiodic $ \ Mathbb Z^2 $ ACTION，我们表明$ L_2 $不是双卵巢群体的联合射手。我们证明，如果$α$，$β\ in（0,1）$是不合理的，$t_α$和$t_β$ ty $ l_1（\ mathbb t）$诱导了相应的旋转，那么在$ c（\ mathbb t）$ in Cobund $ cobundies not cobundies not coob cobbund cobbb in cobundies in $ c（\ mathbb t）中有共同的coboundaries（ t）$）。
Let $T$ and $S$ be commuting contractions on a Banach space $X$. The elements of $(I-T)(I-S)X$ are called {\it double coboundaries}, and the elements of $(I-T)X \cap (I-S)X$ are called {\it joint cobundaries}. For $U$ and $V$ the unitary operators induced on $L_2$ by commuting invertible measure preserving transformations which generate an aperiodic $\mathbb Z^2$-action, we show that there are joint coboundaries in $L_2$ which are not double coboundaries. We prove that if $α$,$β\in (0,1)$ are irrational, with $T_α$ and $T_β$ induced on $L_1(\mathbb T)$ by the corresponding rotations, then there are joint coboundaries in $C(\mathbb T)$ which are not measurable double cobundaries (hence not double coboundaries in $L_1(\mathbb T)$).
