Decomposing algebraic m-isometric tuples

TL;DR

This paper demonstrates that finite-dimensional algebraic m-isometric tuples can be decomposed into a spherical isometry and a nilpotent tuple, extending to hereditary roots of multivariable polynomials.

Contribution

It introduces a decomposition method for algebraic m-isometric tuples, linking them to spherical isometries and nilpotent tuples, with applications to algebraic operator tuples.

Findings

Finite-dimensional m-isometric tuples decompose into spherical isometry plus nilpotent tuple.

The approach applies to algebraic operators that are hereditary roots of multivariable polynomials.

Provides a structural understanding of algebraic m-isometric tuples.

Abstract

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.