Our aim in this paper is to consider a generalization of the concept of n-quasi-m-isometric operators of a single operator done in Mahmoud Sid Ahmed et al. (Results Math 73:511–531, 2018) and Mechri and Mahmoud Sid Ahmed (Oper Matrices 14(1): 145–157, 2020) to the multi-dimensional operators. We discuss the most interesting results concerning these classes of tuples of operators by extending some results obtained in several recent papers for a single operator.

中文翻译：

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$$(n_1,\ldots ,n_p)$$-quasi-m-isometric 换算元组在 Hilbert 空间上

我们在本文中的目的是考虑对 Mahmoud Sid Ahmed 等人完成的单个算子的 n-quasi-m-isometric 算子概念的推广。（Results Math 73:511–531, 2018）以及 Mechri 和 Mahmoud Sid Ahmed（Oper Matrices 14(1): 145–157, 2020）到多维运算符。我们通过扩展最近几篇论文中针对单个运算符获得的一些结果，讨论了关于这些运算符元组类别的最有趣的结果。