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

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.

19 pages and 4 figures