Lower and upper bounds of joint $(f,\delta)$-numerical radius functions

TL;DR

This paper extends classical joint numerical radius results to the joint $(f, ext{delta})$-numerical radius, providing new bounds and estimates for sectorial operators in Hilbert spaces.

Contribution

It introduces novel bounds for the $(f, ext{delta})$-numerical radius, expanding the theoretical framework for sectorial operators.

Findings

Derived new lower bounds for $(f, ext{delta})$-numerical radius

Established upper bounds for sectorial operators

Extended classical results to a broader operator class

Abstract

In this study, the classical results on the joint numerical radius for $n$-tuples of Hilbert space operators are extended to the setting of the joint $(f,\delta)$-numerical radius. New and diverse contributions to this area are provided, including novel estimates for the lower and upper bounds of the $(f,\delta)$-numerical radius in the context of sectorial operators.