论文标题
关于无限基质产品的界限，该产品具有两组矩阵的交替因素
On the boundedness of infinite matrix products with alternating factors from two sets of matrices
论文作者
论文摘要
我们考虑矩阵产品$ a_ {n} b_ {n} \ cdots a_ {1} b_ {1} $的界限问题，并带有两组矩阵的因素，$ a_ {i} \ in \ in \ mathscr {a} $ {a} $和$ b_} $ \ {b_ {i} \} $。假定对于任何矩阵$ \ {a_ {a {i} \} $，都有一系列矩阵$ \ {b_ {i} \} $，矩阵products $ \ \ {a_ {n} b_ {n} b_ {n} \ cdots $ a_ {1} b_ {1} \} _ {n = 1}^{\ infty} $ norm限制。描述了某些情况，在这种情况下，在这种情况下，矩阵产品$ a_ {n} b_ {n} \ cdots a_ {1} b_ {1} b_ {1} $是均匀界限的，也就是说，$ \ | a_ {n} b_ {n} b_ {n} n} \ cdots a_ _ __ {1} $ nrumber wer $ c> 0 $是一个常数，独立于序列$ \ {a_ {i} \} $和相应的序列$ \ {b_ {i} \} $。在一般情况下，相应陈述的有效性问题保持开放。
We consider the question of the boundedness of matrix products $A_{n}B_{n}\cdots A_{1}B_{1}$ with factors from two sets of matrices, $A_{i}\in\mathscr{A}$ and $B_{i}\in\mathscr{B}$, due to an appropriate choice of matrices $\{B_{i}\}$. It is assumed that for any sequence of matrices $\{A_{i}\}$ there is a sequence of matrices $\{B_{i}\}$ for which the sequence of matrix products $\{A_{n}B_{n}\cdots A_{1}B_{1}\}_{n=1}^{\infty}$ is norm bounded. Some situations are described in which in this case the norms of matrix products $A_{n}B_{n}\cdots A_{1}B_{1}$ are uniformly bounded, that is, $\|A_{n}B_{n}\cdots A_{1}B_{1}\|\le C$ for all natural numbers $n$, where $C>0$ is some constant independent of the sequence $\{A_{i}\}$ and the corresponding sequence $\{B_{i}\}$. In the general case, the question of the validity of the corresponding statement remains open.
