论文标题
某些操作员的不变子空间，并具有重现内核对应关系的应用
Invariant subspaces for certain tuples of operators with applications to reproducing kernel correspondences
论文作者
论文摘要
Popescu，Muhly-Solel开发的技术以及对加权转移产生的代数的好处，用于推广Sarkar和Bhattacharjee-Eschmeier-keshari-sarkar的范围，以相关的膨胀和不变的子区域用于接通运营商的tum tum tum。在该论文中，作者证明了通勤元组的beurling-lax-halmos类型结果$ t =（t_1，\ ldots，t_d）$ contrictive and Pure pure;那是$φ_t（i）\ leq i $和$φ_t^n（i）\ searrow 0 $ where $$φ_t（a）=σ_it_iat_i^*。$$在这里我们将其一些结果推广到上下班$ t $ t $ t $ t满足类似条件，但要满足类似的条件，但是for $ $ $ q_t（a）=σ_=σ_ \ Mathbb {f}^+_ d} x_ {|α|}t_αat_α^*$$其中$ \ {x_k \} $是满足某些自然条件的非负数的序列（其中$t_α=t_α=t_α= t_ = t_ = t_ {α（α（α（1）}}）t_ \ cdots t_（\ cdots t_ t_α（k）$ $ | $ |实际上，我们处理更一般的情况，在这种情况下，每个$ x_k $都被$ d^k \ times d^k $矩阵替换。我们还将这些结果应用于某些复制内核对应关系的子空间$ e_k $（与Maps-valued内核$ K $相关联），这些子空间是在坐标函数给出的乘数下不变的。
The techniques developed by Popescu, Muhly-Solel and Good for the study of algebras generated by weighted shifts are applied to generalize results of Sarkar and of Bhattacharjee-Eschmeier-Keshari-Sarkar concerning dilations and invariant subspaces for commuting tuples of operators. In that paper the authors prove Beurling-Lax-Halmos type results for commuting tuples $T=(T_1,\ldots,T_d)$ operators that are contractive and pure; that is $Φ_T(I)\leq I$ and $Φ_T^n(I)\searrow 0$ where $$Φ_T(a)=Σ_i T_iaT_i^*.$$ Here we generalize some of their results to commuting tuples $T$ satisfying similar conditions but for $$Φ_T(a)=Σ_{α\in \mathbb{F}^+_d} x_{|α|}T_αaT_α^*$$ where $\{x_k\}$ is a sequence of non negative numbers satisfying some natural conditions (where $T_α=T_{α(1)}\cdots T_{α(k)}$ for $k=|α|$). In fact, we deal with a more general situation where each $x_k$ is replaced by a $d^k\times d^k$ matrix. We also apply these results to subspaces of certain reproducing kernel correspondences $E_K$ (associated with maps-valued kernels $K$) that are invariant under the multipliers given by the coordinate functions.
