We show that any m-isometric tuples of commuting operators on a finite dimensional Hilbert space can be decomposed as a sum of a spherical isometry and a commuting nilpotent tuple. Our approach applies as well to tuples of algebraic operators that are hereditary roots of polynomials in several variables.

中文翻译：

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分解代数等距元组

我们表明，有限维希尔伯特空间上交换算子的任何 m 等距元组都可以分解为球面等距和交换幂零元组的和。我们的方法也适用于代数运算符的元组，它们是多个变量中多项式的遗传根。