Spectral mapping theorem and the Taylor spectrum

TL;DR

This paper extends the spectral mapping theorem for the Taylor spectrum from doubly commuting pairs to commuting n-tuples of operators, broadening the theorem's applicability in operator theory.

Contribution

The paper generalizes the spectral mapping theorem for the Taylor spectrum to include commuting n-tuples, expanding previous results limited to pairs of operators.

Findings

Spectral mapping theorem holds for commuting n-tuples of operators.

Extension of previous results from pairs to n-tuples.

Broadens understanding of the Taylor spectrum in multivariable operator theory.

Abstract

In [6] Cho and Tanahashi showe new spectral mapping theorem of the taylor spectrum for doubly commuting pairs of p-hyponormal operators and log-hyponormal operators. In this paper, we will show that same spectral mapping theorem holds for commuting n-tuples.