论文标题
组合Tsirelson空间的异构体
Isometries of combinatorial Tsirelson spaces
论文作者
论文摘要
我们扩展了在tsirelson-type空间上表征异构体的现有结果$ t \ big [\ frac {1} {n}，\ nathcal {s} _1 \ big] $（$ n \ in \ m athbb {n}，n \ geq 2 $），n \ geq 2 $} （$θ\ in \ big（0，\ frac {1} {2} \ big] $，$ 1 \leqslantα<ω__1$），其中$ \ MATHCAL {s}_α$表示Schreier的订单$α$。 我们证明，$ t [θ，\ nathcal {s} _1] $（$θ\ in \ big（0，\ frac {1} {2} \ big] $）的每个等轴测图取决于第一个$ \lceilθ^{ - 1} \ rceil a-rceIr can-rceIr can-rceIrt a-rceIrt a-rceIrt a-rceIrt a-rceIrt a cansion a-can-rceIrt a-rceIrt a imelts的置换。此外通过向量坐标的签名变换操作实现。
We extend existing results that characterize isometries on the Tsirelson-type spaces $T\big[\frac{1}{n}, \mathcal{S}_1\big]$ ($n\in \mathbb{N}, n\geq 2$) to the class $T[θ, \mathcal{S}_α]$ ($θ\in \big(0, \frac{1}{2}\big]$, $1\leqslant α< ω_1$), where $\mathcal{S}_α$ denote the Schreier families of order $α$. We prove that every isometry on $T[θ, \mathcal{S}_1]$ ($θ\in \big(0, \frac{1}{2}\big]$) is determined by a permutation of the first $\lceil θ^{-1} \rceil$ elements of the canonical unit basis followed by a possible sign-change of the corresponding coordinates together with a sign-change of the remaining coordinates. Moreover, we show that for the spaces $T[θ, \mathcal{S}_α]$ ($θ\in \big(0, \frac{1}{2}\big]$, $2\leqslant α< ω_1$) the isometries exhibit a more rigid character, namely, they are all implemented by a sign-change operation of the vector coordinates.
