Proof of admissible weights

TL;DR

This paper proves that polynomial weights are admissible, enhancing the understanding of spectral invariance in operator algebra by establishing their validity as permissible weights.

Contribution

It provides a rigorous proof that polynomial weights are admissible, which was previously assumed but not formally demonstrated.

Findings

Polynomial weights are admissible weights.

Supports spectral invariance studies in operator algebra.

Clarifies the role of polynomial weights in spectral analysis.

Abstract

Admissable weight is an important tool for studying spectral invariance in operator algebra. Common admissable weights include polynomial weights and sub exponential weights. This article mainly provides a proof that polynomial weights are permissible weights.