Some spectral properties and convergence of the $ (A,q)$-numerical radius and $ (A,q)$-Crawford number

TL;DR

This paper investigates spectral properties and convergence behaviors of the $(A,q)$-numerical radius and Crawford number in complex semi-Hilbert spaces, providing estimates, tensor product evolutions, and applications with illustrative examples.

Contribution

It introduces new estimates, studies tensor product evolutions, and explores convergence properties of the $(A,q)$-numerical radius and Crawford number in semi-Hilbert spaces.

Findings

Derived bounds for $(A,q)$-numerical radius and Crawford number.

Analyzed tensor product evolutions of operators.

Established convergence properties under $A$-uniform convergence.

Abstract

In this study, some estimates are given for the $ (A,q)$-numerical radius and $ (A,q)$-Crawford number via the $ A$-numerical radius and $ A$-Crawford number for the $ A $-bounded linear operators in any complex semi-Hilbert space, respectively. Then, some evolutions are studied for the tensor product of two operators. Lastly, some convergence properties of the $ (A,q)$-numerical radius and $ (A,q)$-Crawford number, via the $ A$-uniform convergence of operator sequences, are investigated. We also considered several examples to illustrate our results. Finally, a few applications of some operator functions classes are also given.