Refined and generalized numerical radius inequalities for 2 × 2 operator matrices

The Convergence of Some Spectral Characteristics on the Convergent Series

“…We refer the reader to [2,4] for the other basic information and results for the numerical radius. Furthermore, developments on the numerical radius inequalities (1) and (2) can be seen in [3,[5][6][7][8][9] and references there in. Furthermore, remember that the following spectral inclusion holds 𝜎(𝐴) ⊂ 𝑊(𝐴) ̅̅̅̅̅̅̅̅ for the spectrum set 𝜎(𝐴) and numerical range 𝑊(𝐴) of any 𝐴 ∈ 𝐿(𝐻) (see [2,4] for more information).…”

Improved and refined numerical radius inequalities for Hilbert space operators

“…In [9], Bani-Domi and Kittaneh provided a refinement for the inequality (1.3) for the case q = 2 by showing that if S ∈ B(H) and α ∈ [0, 1], then…”

Numerical radius inequalities of $2 \times 2$ operator matrices

“…For A ∈ B(H), let A be the operator norm of A, i.e., A = sup x =1 Ax . For A ∈ B(H), A * denotes the adjoint of A and |A|, |A * | respectively denote the positive part of A, A * , i.e., |A| = (A * A) 1 2 , |A * | = (AA * ) 1 2 . The real part and the imaginary part of A are denoted by ℜ(A) and ℑ(A) respectively so that ℜ(A) = A+A * 2 and ℑ(A) = A−A * 2i .…”