Perturbation of the q-numerical radius of a weighted shift operator

Abstract

We formulate the Taylor series expansion for the q-numerical radius of a weighted shift operator with periodic weights near q = 0. Coefficients up to the fourth order in the expansion are found via the perturbation theory of Hermitian matrices.

On Numerical Radius Bounds Involving Generalized Aluthge Transform

“…For example, upper and lower bounds are utilized to define the operator norm, which plays significantly in solving related problems. The study of the numerical radius of an operator defined on the Hilbert space is in the focus of researchers in these days in studying perturbation, convergence, iterative solution methods, and integrative methods, etc, see [1][2][3][4][5][6][7][8][9]. In this regard, the numerical radius inequality stated in (3) is studied extensively by various mathematicians, see [10][11][12][13][14][15][16][17][18][19][20][21].…”

“…The study of the numerical radius of an operator defined on the Hilbert space is in the focus of researchers in these days in studying perturbation, convergence, iterative solution methods, and integrative methods, etc, see [1][2][3][4][5][6][7][8][9]. In this regard, the numerical radius inequality stated in (3) is studied extensively by various mathematicians, see [10][11][12][13][14][15][16][17][18][19][20][21]. Actually, it is interesting for the researchers to get refinements and generalizations of this inequality [22][23][24][25][26][27].…”